Homological Algebra of Semimodules and Semicontramodules: Semi-infinite Homological Algebra of Associative Algebraic Structures [Paperback]

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.

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)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.ló¬