Published by American Mathematical Society (2006)

ISBN 10: 0821839071 ISBN 13: 9780821839072

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**Item Description: **American Mathematical Society, 2006. Hardcover. Book Condition: New. Brand new. We distribute directly for the publisher. An important idea in the work of G.-C. Rota is that certain combinatorial objects give rise to Hopf algebras that reflect the manner in which these objects compose and decompose. Recent work has seen the emergence of several interesting Hopf algebras of this kind, which connect diverse subjects such as combinatorics, algebra, geometry, and theoretical physics. This monograph presents a novel geometric approach using Coxeter complexes and the projection maps of Tits for constructing and studying many of these objects as well as new ones. The first three chapters introduce the necessary background ideas making this work accessible to advanced graduate students. The later chapters culminate in a unified and conceptual construction of several Hopf algebras based on combinatorial objects which emerge naturally from the geometric viewpoint. This work lays a foundation and provides new insights for further development of the subject. Bookseller Inventory # 1005110160

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**Item Description: **Betascript Publishing. Paperback. Book Condition: new. BRAND NEW PRINT ON DEMAND., Marcelo Aguiar Quarterole, Emory Christer. Bookseller Inventory # B9786136853802

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Published by American Mathematical Society

ISBN 10: 0821839071 ISBN 13: 9780821839072

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**Item Description: **American Mathematical Society. Hardcover. Book Condition: New. Bookseller Inventory # DADAX0821839071

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Published by American Mathematical Society, United States (2011)

ISBN 10: 0821853546 ISBN 13: 9780821853542

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**Item Description: **American Mathematical Society, United States, 2011. Paperback. Book Condition: New. Reprint. 251 x 175 mm. Language: English Brand New Book. Bookseller Inventory # AAN9780821853542

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Published by American Mathematical Society, United States (2011)

ISBN 10: 0821853546 ISBN 13: 9780821853542

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**Item Description: **American Mathematical Society, United States, 2011. Paperback. Book Condition: New. Reprint. 251 x 175 mm. Language: English Brand New Book. An important idea in the work of G.-C. Rota is that certain combinatorial objects give rise to Hopf algebras that reflect the manner in which these objects compose and decompose. Recent work has seen the emergence of several interesting Hopf algebras of this kind, which connect diverse subjects such as combinatorics, algebra, geometry, and theoretical physics. This monograph presents a novel geometric approach using Coxeter complexes and the projection maps of Tits for constructing and studying many of these objects as well as new ones. The first three chapters introduce the necessary background ideas making this work accessible to advanced graduate students. The later chapters culminate in a unified and conceptual construction of several Hopf algebras based on combinatorial objects which emerge naturally from the geometric viewpoint. This work lays a foundation and provides new insights for further development of the subject. Bookseller Inventory # AAN9780821853542

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Published by American Mathematical Society

ISBN 10: 0821853546 ISBN 13: 9780821853542

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**Item Description: **American Mathematical Society. Book Condition: New. pp. 181. Bookseller Inventory # 0650459519

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Published by American Mathematical Society

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ISBN 10: 0821839071 ISBN 13: 9780821839072

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Published by American Mathematical Society

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Published by American Mathematical Society, (2010)

ISBN 10: 0821847767 ISBN 13: 9780821847763

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**Item Description: **American Mathematical Society, 2010. Pappband. Book Condition: Gut. 784 Seiten guter Zustand, Ecke leicht gestaucht M154 Sprache: en Gewicht in Gramm: 1530. Bookseller Inventory # 53580

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Published by American Mathematical Society

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Published by American Mathematical Society

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Published by American Mathematical Society (2010)

ISBN 10: 0821847767 ISBN 13: 9780821847763

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**Item Description: **American Mathematical Society, 2010. Hardcover. Book Condition: New. Brand new. We distribute directly for the publisher. This research monograph integrates ideas from category theory, algebra and combinatorics. It is organized in three parts.Part I belongs to the realm of category theory. It reviews some of the foundational work of Bénabou, Eilenberg, Kelly and Mac Lane on monoidal categories and of Joyal and Street on braided monoidal categories, and proceeds to study higher monoidal categories and higher monoidal functors. Special attention is devoted to the notion of a bilax monoidal functor which plays a central role in this work.Combinatorics and geometry are the theme of Part II. Joyal's species constitute a good framework for the study of algebraic structures associated to combinatorial objects. This part discusses the category of species focusing particularly on the Hopf monoids therein. The notion of a Hopf monoid in species parallels that of a Hopf algebra and reflects the manner in which combinatorial structures compose and decompose. Numerous examples of Hopf monoids are given in the text. These are constructed from combinatorial and geometric data and inspired by ideas of Rota and Tits' theory of Coxeter complexes.Part III is of an algebraic nature and shows how ideas in Parts I and II lead to a unified approach to Hopf algebras. The main step is the construction of Fock functors from species to graded vector spaces. These functors are bilax monoidal and thus translate Hopf monoids in species to graded Hopf algebras. This functorial construction of Hopf algebras encompasses both quantum groups and the Hopf algebras of recent prominence in the combinatorics literature. Bookseller Inventory # 1011190028

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Published by American Mathematical Society, United States (2010)

ISBN 10: 0821847767 ISBN 13: 9780821847763

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**Item Description: **American Mathematical Society, United States, 2010. Hardback. Book Condition: New. 264 x 188 mm. Language: English Brand New Book. This research monograph integrates ideas from category theory, algebra and combinatorics. It is organised in three parts. Part I belongs to the realm of category theory. It reviews some of the foundational work of Benabou, Eilenberg, Kelly and Mac Lane on monoidal categories and of Joyal and Street on braided monoidal categories, and proceeds to study higher monoidal categories and higher monoidal functors. Special attention is devoted to the notion of a bilax monoidal functor which plays a central role in this work. Combinatorics and geometry are the theme of Part II. Joyal s species constitute a good framework for the study of algebraic structures associated to combinatorial objects. This part discusses the category of species focusing particularly on the Hopf monoids therein. The notion of a Hopf monoid in species parallels that of a Hopf algebra and reflects the manner in which combinatorial structures compose and decompose. Numerous examples of Hopf monoids are given in the text. These are constructed from combinatorial and geometric data and inspired by ideas of Rota and Tits theory of Coxeter complexes. Part III is of an algebraic nature and shows how ideas in Parts I and II lead to a unified approach to Hopf algebras. The main step is the construction of Fock functors from species to graded vector spaces. These functors are bilax monoidal and thus translate Hopf monoids in species to graded Hopf algebras. This functorial construction of Hopf algebras encompasses both quantum groups and the Hopf algebras of recent prominence in the combinatorics literature. The monograph opens a vast new area of research. It is written with clarity and sufficient detail to make it accessible to advanced graduate students. Titles in this series are co-published with the Centre de Recherches Mathematiques.|This research monograph integrates ideas from category theory, algebra and combinatorics. It is organised in three parts. Part I belongs to the realm of category theory. It reviews some of the foundational work of Benabou, Eilenberg, Kelly and Mac Lane on monoidal categories and of Joyal and Street on braided monoidal categories, and proceeds to study higher monoidal categories and higher monoidal functors. Special attention is devoted to the notion of a bilax monoidal functor which plays a central role in this work. Combinatorics and geometry are the theme of Part II. Joyal s species constitute a good framework for the study of algebraic structures associated to combinatorial objects. This part discusses the category of species focusing particularly on the Hopf monoids therein. The notion of a Hopf monoid in species parallels that of a Hopf algebra and reflects the manner in which combinatorial structures compose and decompose. Numerous examples of Hopf monoids are given in the text. These are constructed from combinatorial and geometric data and inspired by ideas of Rota and Tits theory of Coxeter complexes. Part III is of an algebraic nature and shows how ideas in Parts I and II lead to a unified approach to Hopf algebras. The main step is the construction of Fock functors from species to graded vector spaces. These functors are bilax monoidal and thus translate Hopf monoids in species to graded Hopf algebras. This functorial construction of Hopf algebras encompasses both quantum groups and the Hopf algebras of recent prominence in the combinatorics literature. The monograph opens a vast new area of research. It is written with clarity and sufficient detail to make it accessible to advanced graduate students. Titles in this series are co-published with the Centre de Recherches Mathematiques. Bookseller Inventory # AAN9780821847763

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Published by American Mathematical Society, United States (2010)

ISBN 10: 0821847767 ISBN 13: 9780821847763

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From: The Book Depository (Slough, United Kingdom)

**Item Description: **American Mathematical Society, United States, 2010. Hardback. Book Condition: New. 264 x 188 mm. Language: English Brand New Book. This research monograph integrates ideas from category theory, algebra and combinatorics. It is organised in three parts. Part I belongs to the realm of category theory. It reviews some of the foundational work of Benabou, Eilenberg, Kelly and Mac Lane on monoidal categories and of Joyal and Street on braided monoidal categories, and proceeds to study higher monoidal categories and higher monoidal functors. Special attention is devoted to the notion of a bilax monoidal functor which plays a central role in this work. Combinatorics and geometry are the theme of Part II. Joyal s species constitute a good framework for the study of algebraic structures associated to combinatorial objects. This part discusses the category of species focusing particularly on the Hopf monoids therein. The notion of a Hopf monoid in species parallels that of a Hopf algebra and reflects the manner in which combinatorial structures compose and decompose. Numerous examples of Hopf monoids are given in the text. These are constructed from combinatorial and geometric data and inspired by ideas of Rota and Tits theory of Coxeter complexes. Part III is of an algebraic nature and shows how ideas in Parts I and II lead to a unified approach to Hopf algebras. The main step is the construction of Fock functors from species to graded vector spaces. These functors are bilax monoidal and thus translate Hopf monoids in species to graded Hopf algebras. This functorial construction of Hopf algebras encompasses both quantum groups and the Hopf algebras of recent prominence in the combinatorics literature. The monograph opens a vast new area of research. It is written with clarity and sufficient detail to make it accessible to advanced graduate students. Titles in this series are co-published with the Centre de Recherches Mathematiques.|This research monograph integrates ideas from category theory, algebra and combinatorics. It is organised in three parts. Part I belongs to the realm of category theory. It reviews some of the foundational work of Benabou, Eilenberg, Kelly and Mac Lane on monoidal categories and of Joyal and Street on braided monoidal categories, and proceeds to study higher monoidal categories and higher monoidal functors. Special attention is devoted to the notion of a bilax monoidal functor which plays a central role in this work. Combinatorics and geometry are the theme of Part II. Joyal s species constitute a good framework for the study of algebraic structures associated to combinatorial objects. This part discusses the category of species focusing particularly on the Hopf monoids therein. The notion of a Hopf monoid in species parallels that of a Hopf algebra and reflects the manner in which combinatorial structures compose and decompose. Numerous examples of Hopf monoids are given in the text. These are constructed from combinatorial and geometric data and inspired by ideas of Rota and Tits theory of Coxeter complexes. Part III is of an algebraic nature and shows how ideas in Parts I and II lead to a unified approach to Hopf algebras. The main step is the construction of Fock functors from species to graded vector spaces. These functors are bilax monoidal and thus translate Hopf monoids in species to graded Hopf algebras. This functorial construction of Hopf algebras encompasses both quantum groups and the Hopf algebras of recent prominence in the combinatorics literature. The monograph opens a vast new area of research. It is written with clarity and sufficient detail to make it accessible to advanced graduate students. Titles in this series are co-published with the Centre de Recherches Mathematiques. Bookseller Inventory # AAN9780821847763

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Published by Amer Mathematical Society (2010)

ISBN 10: 0821847767 ISBN 13: 9780821847763

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**Item Description: **Amer Mathematical Society, 2010. Hardcover. Book Condition: Brand New. 784 pages. 10.00x7.00x1.75 inches. In Stock. Bookseller Inventory # __0821847767

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Published by American Mathematical Society

ISBN 10: 0821847767 ISBN 13: 9780821847763

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**Item Description: **American Mathematical Society. Book Condition: New. pp. 784. Bookseller Inventory # 062149705

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Published by American Mathematical Society

ISBN 10: 0821847767 ISBN 13: 9780821847763

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**Item Description: **American Mathematical Society. Book Condition: New. pp. 784. Bookseller Inventory # 5734292

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