Homological Algebra of Semimodules and Semicontramodules

Semi-infinite Homological Algebra of Associative Algebraic Structures

  • Leonid┬áPositselski

Part of the Monografie Matematyczne book series (MONOGRAFIE, volume 70)

Table of contents

  1. Front Matter
    Pages i-xxiv
  2. Leonid Positselski, Sergey Arkhipov, Dmitriy Rumynin
    Pages 1-24
  3. Leonid Positselski, Sergey Arkhipov, Dmitriy Rumynin
    Pages 25-38
  4. Leonid Positselski, Sergey Arkhipov, Dmitriy Rumynin
    Pages 39-55
  5. Leonid Positselski, Sergey Arkhipov, Dmitriy Rumynin
    Pages 57-75
  6. Leonid Positselski, Sergey Arkhipov, Dmitriy Rumynin
    Pages 77-88
  7. Leonid Positselski, Sergey Arkhipov, Dmitriy Rumynin
    Pages 89-105
  8. Leonid Positselski, Sergey Arkhipov, Dmitriy Rumynin
    Pages 107-124
  9. Leonid Positselski, Sergey Arkhipov, Dmitriy Rumynin
    Pages 125-141
  10. Leonid Positselski, Sergey Arkhipov, Dmitriy Rumynin
    Pages 143-167
  11. Leonid Positselski, Sergey Arkhipov, Dmitriy Rumynin
    Pages 169-182
  12. Leonid Positselski, Sergey Arkhipov, Dmitriy Rumynin
    Pages 183-192
  13. Leonid Positselski, Sergey Arkhipov, Dmitriy Rumynin
    Pages 193-225
  14. Back Matter
    Pages 227-352

About this book

Introduction

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.

Keywords

Algebraic structure Category theory Cohomology Functoriality Homological algebra Koszul duality Semicontramodule Semimodule

Authors and affiliations

  • Leonid┬áPositselski
    • 1
  1. 1.Problems (IITP)Institute for Information TransmissionMoskvaRussian Federation

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-0346-0436-9
  • Copyright Information Springer Basel AG 2010
  • Publisher Name Springer, Basel
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-0346-0435-2
  • Online ISBN 978-3-0346-0436-9
  • About this book