Homological Algebra of Semimodules and Semicontramodules - Semi-infinite Homological Algebra of Associative Algebraic Structures (Hardcover, 2010 ed.)

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.

General

Imprint:	Birkhauser Verlag AG
Country of origin:	Switzerland
Series:	Monografie Matematyczne, 70
Release date:	September 2010
First published:	2010
Authors:	Leonid Positselski
Dimensions:	235 x 155 x 25mm (L x W x T)
Format:	Hardcover
Pages:	352
Edition:	2010 ed.
ISBN-13:	978-3-03-460435-2
Categories:	Books > Science & Mathematics > Mathematics > Algebra > General
LSN:	3-03-460435-1
Barcode:	9783034604352

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