Cyclic Homology of Strong Smash Product Algebras

Details Cyclic Homology of Strong Smash Product Algebras Cyclic Homology of Strong Smash Product Algebras

2010-08-15

arxiv.org/abs/1008.2504v1

J. Reine und Angew. Math. Heft 663 (2012), 177-207

Mathematics

Quantum Algebra

Journal f\"ur die Reine und Angewandte Mathematik (2010)

Scientific paper

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 $A\natural B$ whose diagonal cyclic module $\Delta_{\bullet}(A\natural B)$ 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.

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