Cyclic operads and cyclic homology TeX Export

@inbook{citeulike:466571, abstract = { This is an important foundational paper which generalizes the notion of an operad to the situation when its inputs are indistinguishable from its output, i.e., when the action of the symmetric group \$S\sb n\$ on the \$n\$th component \$\scr O (n)\$ of the operad extends to an action of \$S\sb {n+1}\$ in a way compatible with operad compositions. Such operads are called cyclic by the authors. At the level of algebras over operads, an algebra over a cyclic operad usually indicates the presence of an invariant bilinear form. The main part of the paper is the definition and study of cyclic homology of an algebra over a cyclic operad. This homology theory generalizes the cyclic homology of associative algebras. Specifying the definition to different cyclic operads, one can now define cyclic homology of commutative, Lie, and Poisson algebras. These examples are also discussed in the paper. <P> {For the entire collection see <A HREF="/msnmain?fn=105\&fmt=doc\&r=1\&pg1=CNO\&s1=1358611\&loc=fromrevtext">MR1358611 (96f:00038)</A>.} }, address = {Cambridge, MA}, author = {Getzler, E. and Kapranov, M. M.}, booktitle = {Geometry, topology, \& physics}, citeulike-article-id = {466571}, citeulike-linkout-0 = {http://www.ams.org/mathscinet-getitem?mr=1358617}, keywords = {cyclic\_cohomology, cyclic\_operads, ncg, operads}, mrnumber = {MR1358617}, pages = {167--201}, posted-at = {2006-01-17 01:41:50}, priority = {2}, publisher = {Internat. Press}, series = {Conf. Proc. Lecture Notes Geom. Topology, IV}, title = {Cyclic operads and cyclic homology}, url = {http://www.ams.org/mathscinet-getitem?mr=1358617}, year = {1995} }

TY - CHAP ID - citeulike:466571 L3 - citeulike-article-id:466571 N2 - This is an important foundational paper which generalizes the notion of an operad to the situation when its inputs are indistinguishable from its output, i.e., when the action of the symmetric group $S\sb n$ on the $n$th component $\scr O (n)$ of the operad extends to an action of $S\sb {n+1}$ in a way compatible with operad compositions. Such operads are called cyclic by the authors. At the level of algebras over operads, an algebra over a cyclic operad usually indicates the presence of an invariant bilinear form. The main part of the paper is the definition and study of cyclic homology of an algebra over a cyclic operad. This homology theory generalizes the cyclic homology of associative algebras. Specifying the definition to different cyclic operads, one can now define cyclic homology of commutative, Lie, and Poisson algebras. These examples are also discussed in the paper. <P> {For the entire collection see <A HREF="/msnmain?fn=105&fmt=doc&r=1&pg1=CNO&s1=1358611&loc=fromrevtext">MR1358611 (96f:00038)</A>.} SE - Conf. Proc. Lecture Notes Geom. Topology, IV AD - Cambridge, MA EP - 201 TI - Cyclic operads and cyclic homology PB - Internat. Press T2 - Geometry, topology, \& physics SP - 167 KW - cyclic_cohomology KW - cyclic_operads KW - ncg KW - operads AU - Getzler, E AU - Kapranov, MM PY - 1995/// UR - http://www.ams.org/mathscinet-getitem?mr=1358617 ER -