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

2000/11/29 by R. Akbarpour, Akbarpour, R., M. Khalkhali +1
Mathematics · #FOS: Mathematics #K-Theory and Homology (math.KT) #math.KT

paper · pdf · doi:10.48550/arxiv.math/0011248

Final version, to appear in "Crelle's Journal"

arxiv created 2002/12/12 · arxiv updated 2009/11/30

Abstract

We introduce the cylindrical module A \natural H, where H is a Hopf algebra and A is a Hopf module algebra over H. We show that there exists an isomorphism between C_\bullet(A^op \rtimes H^cop) the cyclic module of the crossed product algebra A^op \rtimes H^cop , and Δ(A \natural H) , the cyclic module related to the diagonal of A \natural H. If S, the antipode of H, is invertible it follows that C_\bullet(A \rtimes H) ≃ Δ(A^op \natural H^cop). When S is invertible, we approximate HC_\bullet(A \rtimes H) by a spectral sequence and give an interpretation of E⁰, E¹ and E² terms of this spectral sequence.

Related

• Cyclic Homology of Hopf Comodule Algebras and Hopf Module Coalgebras
• On the Cyclic Homology of Hopf Crossed Products
• Cyclic homology of Hopf Galois extensions and Hopf algebras
• Cyclic homology of crossed products
• (Co)homology of Crossed Products by Weak Hopf Algebras