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Homological Algebra of Semimodules and Semicontramodules

Homological Algebra of Semimodules and Semicontramodules


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About the Book

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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Product Details
  • ISBN-13: 9783034604352
  • Publisher: Birkhauser
  • Publisher Imprint: Birkhauser
  • Depth: 25
  • Height: 234 mm
  • No of Pages: 352
  • Series Title: Monografie Matematyczne
  • Sub Title: Semi-Infinite Homological Algebra of Associative Algebraic Structures
  • Width: 155 mm
  • ISBN-10: 3034604351
  • Publisher Date: 29 Sep 2010
  • Binding: Hardback
  • Edition: 2010 ed.
  • Language: English
  • Returnable: Y
  • Spine Width: 25 mm
  • Weight: 707 gr


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