Hopf Algebra Equivariant Cyclic Homology and Cyclic Homology of Crossed Product Algebras

By R. Akbarpour, Masoud Khalkhali. 2000

58 citations recorded by the source corpus.

We introduce the cylindrical module $A \natural \mathcal{H}$, where $\mathcal{H}$ is a Hopf algebra and $A$ is a Hopf module algebra over $\mathcal{H}$. We show that there exists an isomorphism between $\mathsf{C}_{\bullet}(A^{op} \rtimes \mathcal{H}^{cop})$ the cyclic module of the crossed product algebra $A^{op} \rtimes \mathcal{H}^{cop} $, and $\Delta(A \natural \mathcal{H}) $, the cyclic module related to the diagonal of $A \natural \mathcal{H}$. If $S$, the antipode of $\mathcal{H}$, is invertible it follows that $\mathsf{C}_{\bullet}(A \rtimes \mathcal{H}) \simeq \Delta(A^{op} \natural \mathcal{H}^{cop})$. When $S$ is invertible, we approximate $HC_{\bullet}(A \rtimes \mathcal{H})$ by a spectral sequence and give an interpretation of $ \mathsf{E}^0, \mathsf{E}^1$ and $\mathsf{E}^2 $ terms of this spectral sequence.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9d3a50b5d18e77df4b5e4b858075526188fd50bf

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Lectures on Noncommutative Geometry (2005, background): “One generator is the class of the trivial idempotent [1].”
Hopf-cyclic homology and cohomology with coefficients (2003, methodology): “Then we arrive at the construction considered in [ 1 ].”