Monografie Matematyczne

Homological Algebra of Semimodules and Semicontramodules

Semi-infinite Homological Algebra of Associative Algebraic Structures

Authors: Positselski, Leonid

  • Provides comprehensive coverage on semi-infinite homology and cohomology of associative algebraic structures
  • Features rich representation-theoretic and algebro-geometric examples and applications
  • Coverage includes exotic derived categories, contramodules, semialgebras, infinite-dimensional Lie algebras, algebraic Harish-Chandra pairs, and locally compact totally disconnected topological groups
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eBook $109.00
price for USA (gross)
  • ISBN 978-3-0346-0436-9
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  • Included format: PDF
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  • Immediate eBook download after purchase
Hardcover $149.00
price for USA
  • ISBN 978-3-0346-0435-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $149.00
price for USA
  • ISBN 978-3-0348-0313-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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.

Reviews

From the reviews:

“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)

Table of contents (12 chapters)

  • Preliminaries and Summary

    Positselski, Leonid (et al.)

    Pages 1-24

  • Semialgebras and Semitensor Product

    Positselski, Leonid (et al.)

    Pages 25-38

  • Derived Functor SemiTor

    Positselski, Leonid (et al.)

    Pages 39-55

  • Semicontramodules and Semihomomorphisms

    Positselski, Leonid (et al.)

    Pages 57-75

  • Derived Functor SemiExt

    Positselski, Leonid (et al.)

    Pages 77-88

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-3-0346-0436-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.00
price for USA
  • ISBN 978-3-0346-0435-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $149.00
price for USA
  • ISBN 978-3-0348-0313-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Homological Algebra of Semimodules and Semicontramodules
Book Subtitle
Semi-infinite Homological Algebra of Associative Algebraic Structures
Authors
Series Title
Monografie Matematyczne
Series Volume
70
Copyright
2010
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Basel
eBook ISBN
978-3-0346-0436-9
DOI
10.1007/978-3-0346-0436-9
Hardcover ISBN
978-3-0346-0435-2
Softcover ISBN
978-3-0348-0313-7
Series ISSN
0077-0507
Edition Number
1
Number of Pages
XXIV, 352
Topics