Hochschild homology of iterate skew polynomial rings

2002/05/08 by Jorge A. Guccione, Guccione, Jorge A., Juan J. Guccione +1
Mathematics · #16E40 #18G99 #FOS: Mathematics #K-Theory and Homology (math.KT) #Quantum Algebra (math.QA) #math.KT #math.QA #msc:16E40 #msc:18G99

paper · pdf · doi:10.48550/arxiv.math/0205087

18 pages

arxiv created 2002/05/08 · arxiv updated 2009/11/30

Abstract

We study the Hochschild homology of the iterated skew polynomial rings introduced by D. Jordan in ``A simple localization of the quantized Weyl algebra''. First, we obtain a complex, smaller than the canonical one of Hochschild, given the homology of such an algebra, and then, we study this complex in order to compute the homology of some families of algebras. In particular we compute the homology of some quantum groups, in the generic case.

Related

• On the Hochschild homology of smash biproducts
• On the Hochschild (co)homology of quantum exterior algebras
• Quantum differentiation and chain maps of bimodule complexes
• Homology of quantum linear groups
• Quantization, orbifold cohomology, and Cherednik algebras