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

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dc.creatorAkbarpour, R.
dc.creatorKhalkhali, M.
dc.date2000-11-29
dc.date2002-12-12
dc.date.accessioned2026-07-07T04:38:55Z
dc.date.available2026-07-07T04:38:55Z
dc.descriptionWe 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 $Δ(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 $\mathsf{C}_{\bullet}(A \rtimes \mathcal{H}) \simeq Δ(A^{op} \natural \mathcal{H}^{cop})$. 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.
dc.descriptionFinal version, to appear in "Crelle's Journal"
dc.identifierhttps://arxiv.org/abs/math/0011248
dc.identifierhttp://arxiv.org/abs/math/0011248
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/60464
dc.subjectK-Theory and Homology
dc.titleHopf Algebra Equivariant Cyclic Homology and Cyclic Homology of Crossed Product Algebras
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