Cyclic Homology of Strong Smash Product Algebras

Abstract

For any strong smash product algebra $A{\#}_{{}_R}B$ of two algebras $A$ and $B$ with a bijective morphism $R$ mapping from $B\ot A$ to $A\ot B$, we construct a cylindrical module $A♮B$ whose diagonal cyclic module ${\Delta }_{\bullet }(A♮B)$ is graphically proven to be isomorphic to $C_{\bullet }(A{\#}_{{}_R}B)$ the cyclic module of the algebra. A spectral sequence is established to converge to the cyclic homology of $A{\#}_{{}_R}B$. Examples are provided to show how our results work. Particularly, the cyclic homology of the Pareigis' Hopf algebra is obtained in the way.

Journal für die Reine und Angewandte Mathematik (2010)

References in corpus (2)

• Convex PBW-Type Lyndon Bases and Restricted Two-parameter Quantum Groups of Type B
• Notes on two-parameter quantum groups, (II)

Cited by in corpus (1)

• Cyclic homology of braided Hopf crossed products