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

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...

Πλήρης περιγραφή

Λεπτομέρειες βιβλιογραφικής εγγραφής
Κύριος συγγραφέας: Positselski, Leonid (Συγγραφέας)
Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
Γλώσσα:English
Έκδοση: Basel : Springer Basel, 2010.
Σειρά:Monografie Matematyczne ; 70
Θέματα:
Διαθέσιμο Online:Full Text via HEAL-Link
LEADER 04062nam a22005175i 4500
001 978-3-0346-0436-9
003 DE-He213
005 20151204155539.0
007 cr nn 008mamaa
008 100907s2010 sz | s |||| 0|eng d
020 |a 9783034604369  |9 978-3-0346-0436-9 
024 7 |a 10.1007/978-3-0346-0436-9  |2 doi 
040 |d GrThAP 
050 4 |a QA169 
072 7 |a PBC  |2 bicssc 
072 7 |a PBF  |2 bicssc 
072 7 |a MAT002010  |2 bisacsh 
082 0 4 |a 512.6  |2 23 
100 1 |a Positselski, Leonid.  |e author. 
245 1 0 |a Homological Algebra of Semimodules and Semicontramodules  |h [electronic resource] :  |b Semi-infinite Homological Algebra of Associative Algebraic Structures /  |c by Leonid Positselski. 
264 1 |a Basel :  |b Springer Basel,  |c 2010. 
300 |a XXIV, 352 p.  |b online resource. 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
347 |a text file  |b PDF  |2 rda 
490 1 |a Monografie Matematyczne ;  |v 70 
505 0 |a 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. 
520 |a 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. 
650 0 |a Mathematics. 
650 0 |a Category theory (Mathematics). 
650 0 |a Homological algebra. 
650 0 |a Global analysis (Mathematics). 
650 0 |a Manifolds (Mathematics). 
650 0 |a Differential geometry. 
650 1 4 |a Mathematics. 
650 2 4 |a Category Theory, Homological Algebra. 
650 2 4 |a Global Analysis and Analysis on Manifolds. 
650 2 4 |a Differential Geometry. 
710 2 |a SpringerLink (Online service) 
773 0 |t Springer eBooks 
776 0 8 |i Printed edition:  |z 9783034604352 
830 0 |a Monografie Matematyczne ;  |v 70 
856 4 0 |u http://dx.doi.org/10.1007/978-3-0346-0436-9  |z Full Text via HEAL-Link 
912 |a ZDB-2-SMA 
950 |a Mathematics and Statistics (Springer-11649)