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arXiv · 1008.2504

Cyclic Homology of Strong Smash Product Algebras

Jiao Zhang·Naihong Hu
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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 $A\natural B$ whose diagonal cyclic module $Δ_{\bullet}(A\natural B)$ 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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BibTeXRIS

Jiao Zhang, Naihong Hu. 2010-08-15. Cyclic Homology of Strong Smash Product Algebras. https://arxiv.org/abs/1008.2504

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