Homological Algebra of Semimodules and Semicontramodules - Couverture rigide

Positselski, Leonid

Couverture rigide

ISBN 10 : 3034604351 ISBN 13 : 9783034604352

Editeur : Birkhauser Verlag AG, 2010

Synopsis

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.

A propos du livre

Présentation de l'éditeur

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.

Détails de l'édition

• Éditeur: Birkhauser Verlag AG
• Date d'édition: 2010
• Langue: anglais
• ISBN 10: 3034604351
• ISBN 13: 9783034604352
• Reliure: Relié
• Nombre de pages: 376
• Coordonnées du fabricant: GPSR Kontakt; ProductSafety@springernature.com; ; Tiergartenstr. 17; Heidelberg; 69121; Allemagne