Homological Algebra of Semimodules and Semicontramodules Semi-infinite Homological Algebra of Associative Algebraic Structures /

• Main Author: Positselski, Leonid. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Basel : Springer Basel, 2010.
• Series: Monografie Matematyczne ; 70
• Subjects: Mathematics.; Global analysis.; Global differential geometry.; Global Analysis and Analysis on Manifolds.; Differential Geometry.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-0346-0436-9

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 deriv...

Table of Contents:

• Preface
• Introduction
• 0 Preliminaries and Summary
• 1 Semialgebras and Semitensor Product
• 2 Derived Functor SemiTor
• 3 Semicontramodules and Semihomomorphisms
• 4 Derived Functor SemiExt
• 5 Comodule-Contramodule Correspondence
• 6 Semimodule-Semicontramodule Correspondence
• 7 Functoriality in the Coring
• 8 Functoriality in the Semialgebra
• 9 Closed Model Category Structures
• 10 A Construction of Semialgebras
• 11 Relative Nonhomogeneous Koszul Duality
• Appendix A Contramodules over Coalgebras over Fields
• Appendix B Comparison with Arkhipov's Ext^{ infty/2+*} and Sevostyanov's Tor_{ infty/2+*}
• Appendix C Semialgebras Associated to Harish-Chandra Pairs
• Appendix D Tate Harish-Chandra Pairs and Tate Lie Algebras
• Appendix E Groups with Open Profinite Subgroups
• Appendix F Algebraic Groupoids with Closed Subgroupoids
• Bibliography
• Index.