000 04401nam a22005175i 4500
001 978-3-642-30362-3
003 DE-He213
005 20140220083318.0
007 cr nn 008mamaa
008 120806s2012 gw | s |||| 0|eng d
020 _a9783642303623
_9978-3-642-30362-3
024 7 _a10.1007/978-3-642-30362-3
_2doi
050 4 _aQA169
072 7 _aPBC
_2bicssc
072 7 _aPBF
_2bicssc
072 7 _aMAT002010
_2bisacsh
082 0 4 _a512.6
_223
100 1 _aLoday, Jean-Louis.
_eauthor.
245 1 0 _aAlgebraic Operads
_h[electronic resource] /
_cby Jean-Louis Loday, Bruno Vallette.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2012.
300 _aXXIV, 634 p. 219 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,
_x0072-7830 ;
_v346
505 0 _aPreface -- 1.Algebras, coalgebras, homology -- 2.Twisting morphisms -- 3.Koszul duality for associative algebras -- 4.Methods to prove Koszulity of an algebra -- 5.Algebraic operad -- 6 Operadic homological algebra -- 7.Koszul duality of operads -- 8.Methods to prove Koszulity of an operad -- 9.The operads As and A\infty -- 10.Homotopy operadic algebras -- 11.Bar and cobar construction of an algebra over an operad -- 12.(Co)homology of algebras over an operad -- 13.Examples of algebraic operads -- Apendices: A.The symmetric group -- B.Categories -- C.Trees -- References -- Index -- List of Notation.
520 _aIn many areas of mathematics some “higher operations” are arising. These have become so important that several research projects refer to such expressions. Higher operations form new types of algebras. The key to understanding and comparing them, to creating invariants of their action is operad theory. This is a point of view that is 40 years old in algebraic topology, but the new trend is its appearance in several other areas, such as algebraic geometry, mathematical physics, differential geometry, and combinatorics. The present volume is the first comprehensive and systematic approach to algebraic operads. An operad is an algebraic device that serves to study all kinds of algebras (associative, commutative, Lie, Poisson, A-infinity, etc.) from a conceptual point of view. The book presents this topic with an emphasis on Koszul duality theory. After a modern treatment of Koszul duality for associative algebras, the theory is extended to operads. Applications to homotopy algebra are given, for instance the HomotopyTransfer Theorem. Although the necessary notions of algebra are recalled, readers areexpected to be familiar with elementary homological algebra. Each chapter ends with a helpful summary and exercises. A full chapter is devoted to examples, and numerous figures are included. After an elementary chapter on classical algebra, accessible to undergraduate students, the level increases gradually through the book. However, the authors have done their best to make it suitable for graduate students: three appendices  review the basic results needed in order to understand the various  chapters. Since higher algebra is becoming essential in several research areas like deformation theory, algebraic geometry, representation theory, differential geometry, algebraic combinatorics, and mathematical physics, the book can also be used as a reference work by researchers.  
650 0 _aMathematics.
650 0 _aAlgebra.
650 0 _aAlgebraic topology.
650 0 _aCell aggregation
_xMathematics.
650 1 4 _aMathematics.
650 2 4 _aCategory Theory, Homological Algebra.
650 2 4 _aNon-associative Rings and Algebras.
650 2 4 _aAlgebraic Topology.
650 2 4 _aManifolds and Cell Complexes (incl. Diff.Topology).
700 1 _aVallette, Bruno.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642303616
830 0 _aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,
_x0072-7830 ;
_v346
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-642-30362-3
912 _aZDB-2-SMA
999 _c103162
_d103162