Cyclic homology of the Taft algebras and of their Auslander algebras

2000/09/25 by Rachel Taillefer, Taillefer, Rachel
Mathematics · #16E20 #16E40 #16G70 #16W30 #19A99 #19D55 #57T05 #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #msc:16E20 #msc:16E40 #msc:16G70 #msc:16W30 #msc:19A99 #msc:19D55 #msc:57T05

paper · pdf · doi:10.48550/arxiv.math/0009214

11 pages, 3 figures

arxiv created 2000/09/25 · arxiv updated 2009/11/30

Abstract

In this paper, we compute the cyclic homology of the Taft algebras and of their Auslander algebras. Given a Hopf algebra Λ, the Grothendieck groups of projective Λ-modules and of all Λ-modules are endowed with a ring structure, which in the case of the Taft algebras is commutative (\citeC2, \citeG). We also describe the first Chern character for these algebras.

Related

• Hochschild and cyclic homology of a family of Auslander algebras
• Cyclic homology of Hopf algebras
• A New Cyclic Module for Hopf Algebras
• Cyclic homology of Hopf Galois extensions and Hopf algebras
• Categorified Chern character and cyclic cohomology