This note discusses the cyclic cohomology of a left Hopf algebroid (×_A-Hopf algebra) with coefficients in a right module-left comodule, defined using a straightforward generalisation of the original operators given by Connes and Moscovici for Hopf algebras. Lie-Rinehart homology is a special case of this theory. A generalisation of cyclic duality that makes sense for arbitrary para-cyclic objects yields a dual homology theory. The twisted cyclic homology of an associative algebra provides an example of this dual theory that uses coefficients that are not necessarily stable anti Yetter-Drinfel’d modules.
CYCLIC STRUCTURES IN ALGEBRAIC (CO)HOMOLOGY THEORIES / Kowalzig, Niels; Kraehmer, Ulrich. - In: HOMOLOGY, HOMOTOPY AND APPLICATIONS. - ISSN 1532-0073. - STAMPA. - 13:1(2011), pp. 297-318. [doi:10.4310/HHA.2011.v13.n1.a11]
CYCLIC STRUCTURES IN ALGEBRAIC (CO)HOMOLOGY THEORIES
KOWALZIG, NIELS;
2011
Abstract
This note discusses the cyclic cohomology of a left Hopf algebroid (×_A-Hopf algebra) with coefficients in a right module-left comodule, defined using a straightforward generalisation of the original operators given by Connes and Moscovici for Hopf algebras. Lie-Rinehart homology is a special case of this theory. A generalisation of cyclic duality that makes sense for arbitrary para-cyclic objects yields a dual homology theory. The twisted cyclic homology of an associative algebra provides an example of this dual theory that uses coefficients that are not necessarily stable anti Yetter-Drinfel’d modules.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.