Homological Algebra of Semimodules and Semicontramodules: Semi-infinite Homological Algebra of Associative Algebraic Structures (Monografie Matematyczne)

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9783034604352: Homological Algebra of Semimodules and Semicontramodules: Semi-infinite Homological Algebra of Associative Algebraic Structures (Monografie Matematyczne)
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This book provides comprehensive coverage on semi-infinite homology and cohomology of associative algebraic structures. It features rich representation-theoretic and algebro-geometric examples and applications.

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This monograph deals with semi-infinite homological algebra. Intended as the definitive treatment of the subject of semi-infinite homology and cohomology of associative algebraic structures, it also contains material on the semi-infinite (co)homology of Lie algebras and topological groups, the derived comodule-contramodule correspondence, its application to the duality between representations of infinite-dimensional Lie algebras with complementary central charges, and relative non-homogeneous Koszul duality. The book explains with great clarity what the associative version of semi-infinite cohomology is, why it exists, and for what kind of objects it is defined. Semialgebras, contramodules, exotic derived categories, Tate Lie algebras, algebraic Harish-Chandra pairs, and locally compact totally disconnected topological groups all interplay in the theories developed in this monograph. Contramodules, introduced originally by Eilenberg and Moore in the 1960s but almost forgotten for four decades, are featured prominently in this book, with many versions of them introduced and discussed. Rich in new ideas on homological algebra and the theory of corings and their analogues, this book also makes a contribution to the foundational aspects of representation theory. In particular, it will be a valuable addition to the algebraic literature available to mathematical physicists.

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“The book is written for experts in several areas such as homological algebra, representation theory of Lie algebras and Hopf algebras. The theoretical results are proven with enough detail and with an eye towards specific applications in mind. ... give an excellent overview of the whole book and its connections with the relevant results in the literature.” (Atabey Kaygun, Mathematical Reviews, Issue 2012 c)

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Book Description Springer Basel AG Sep 2010, 2010. Buch. Condition: Neu. Neuware - ThesubjectofthisbookisSemi-In niteAlgebra,ormorespeci cally,Semi-In nite Homological Algebra. The term semi-in nite is loosely associated with objects that can be viewed as extending in both a positive and a negative direction, withsomenaturalpositioninbetween,perhapsde nedupto a nite movement. Geometrically, this would mean an in nite-dimensional variety with a natural class of semi-in nite cycles or subvarieties, having always a nite codimension in each other, but in nite dimension and codimension in the whole variety [37]. (For further instances of semi-in nite mathematics see, e. g. , [38] and [57], and references below. ) Examples of algebraic objects of the semi-in nite type range from certain in nite-dimensional Lie algebras to locally compact totally disconnected topolo- cal groups to ind-schemes of ind-in nite type to discrete valuation elds. From an abstract point of view, these are ind-pro-objects in various categories, often - dowed with additional structures. One contribution we make in this monograph is the demonstration of another class of algebraic objects that should be thought of as semi-in nite , even though they do not at rst glance look quite similar to the ones in the above list. These are semialgebras over coalgebras, or more generally over corings the associative algebraic structures of semi-in nite nature. The subject lies on the border of Homological Algebra with Representation Theory, and the introduction of semialgebras into it provides an additional link with the theory of corings [23], as the semialgebrasare the natural objects dual to corings. 349 pp. Englisch. Seller Inventory # 9783034604352

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Book Description Springer Basel AG Sep 2010, 2010. Buch. Condition: Neu. Neuware - ThesubjectofthisbookisSemi-In niteAlgebra,ormorespeci cally,Semi-In nite Homological Algebra. The term semi-in nite is loosely associated with objects that can be viewed as extending in both a positive and a negative direction, withsomenaturalpositioninbetween,perhapsde nedupto a nite movement. Geometrically, this would mean an in nite-dimensional variety with a natural class of semi-in nite cycles or subvarieties, having always a nite codimension in each other, but in nite dimension and codimension in the whole variety [37]. (For further instances of semi-in nite mathematics see, e. g. , [38] and [57], and references below. ) Examples of algebraic objects of the semi-in nite type range from certain in nite-dimensional Lie algebras to locally compact totally disconnected topolo- cal groups to ind-schemes of ind-in nite type to discrete valuation elds. From an abstract point of view, these are ind-pro-objects in various categories, often - dowed with additional structures. One contribution we make in this monograph is the demonstration of another class of algebraic objects that should be thought of as semi-in nite , even though they do not at rst glance look quite similar to the ones in the above list. These are semialgebras over coalgebras, or more generally over corings the associative algebraic structures of semi-in nite nature. The subject lies on the border of Homological Algebra with Representation Theory, and the introduction of semialgebras into it provides an additional link with the theory of corings [23], as the semialgebrasare the natural objects dual to corings. 349 pp. Englisch. Seller Inventory # 9783034604352

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Book Description Springer Basel AG Sep 2010, 2010. Buch. Condition: Neu. Neuware - ThesubjectofthisbookisSemi-In niteAlgebra,ormorespeci cally,Semi-In nite Homological Algebra. The term semi-in nite is loosely associated with objects that can be viewed as extending in both a positive and a negative direction, withsomenaturalpositioninbetween,perhapsde nedupto a nite movement. Geometrically, this would mean an in nite-dimensional variety with a natural class of semi-in nite cycles or subvarieties, having always a nite codimension in each other, but in nite dimension and codimension in the whole variety [37]. (For further instances of semi-in nite mathematics see, e. g. , [38] and [57], and references below. ) Examples of algebraic objects of the semi-in nite type range from certain in nite-dimensional Lie algebras to locally compact totally disconnected topolo- cal groups to ind-schemes of ind-in nite type to discrete valuation elds. From an abstract point of view, these are ind-pro-objects in various categories, often - dowed with additional structures. One contribution we make in this monograph is the demonstration of another class of algebraic objects that should be thought of as semi-in nite , even though they do not at rst glance look quite similar to the ones in the above list. These are semialgebras over coalgebras, or more generally over corings the associative algebraic structures of semi-in nite nature. The subject lies on the border of Homological Algebra with Representation Theory, and the introduction of semialgebras into it provides an additional link with the theory of corings [23], as the semialgebrasare the natural objects dual to corings. 349 pp. Englisch. Seller Inventory # 9783034604352

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