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.

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This is a monograph in semi-infinite homological algebra, concentrated mostly on the semi-infinite theory of associative algebraic structures, but including also some material on the semi-infinite homology and cohomology of Lie algebras and topological groups. The main objects of study are the double-sided derived functors SemiExt and SemiTor, and the phenomenon of comodule-contramodule correspondence, connecting them with the more conventional, one-sided Ext and CtrTor. Contramodules, introduced originally by Eilenberg and Moore in 1960's but almost forgotten for four decades, play a very prominent role in this book, with many versions of them introduced and discussed. Among other topics considered in the monograph there are the semi-infinite model category structures and the relative nohomogeneous Koszul duality.

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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**Book Description **Springer Basel AG Sep 2010, 2010. Buch. Book Condition: Neu. 233x155x30 mm. 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. Bookseller Inventory # 9783034604352

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**Book Description **Springer Basel AG Sep 2010, 2010. Buch. Book Condition: Neu. 233x155x30 mm. 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. Bookseller Inventory # 9783034604352

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