000 04043nam a22005175i 4500
001 978-3-0346-0436-9
003 DE-He213
005 20160302165625.0
007 cr nn 008mamaa
008 100907s2010 sz | s |||| 0|eng d
020 _a9783034604369
_9978-3-0346-0436-9
024 7 _a10.1007/978-3-0346-0436-9
_2doi
050 4 _aQA169
072 7 _aPBC
_2bicssc
072 7 _aPBF
_2bicssc
072 7 _aMAT002010
_2bisacsh
082 0 4 _a512.6
_223
100 1 _aPositselski, Leonid.
_eauthor.
245 1 0 _aHomological Algebra of Semimodules and Semicontramodules
_h[electronic resource] :
_bSemi-infinite Homological Algebra of Associative Algebraic Structures /
_cby Leonid Positselski.
264 1 _aBasel :
_bSpringer Basel,
_c2010.
300 _aXXIV, 352 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aMonografie Matematyczne ;
_v70
505 0 _aPreface -- 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 _aThis 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 _aMathematics.
650 0 _aCategory theory (Mathematics).
650 0 _aHomological algebra.
650 0 _aGlobal analysis (Mathematics).
650 0 _aManifolds (Mathematics).
650 0 _aDifferential geometry.
650 1 4 _aMathematics.
650 2 4 _aCategory Theory, Homological Algebra.
650 2 4 _aGlobal Analysis and Analysis on Manifolds.
650 2 4 _aDifferential Geometry.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783034604352
830 0 _aMonografie Matematyczne ;
_v70
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-0346-0436-9
912 _aZDB-2-SMA
999 _c191078
_d191078