On the Cyclic Homology of an Algebra Associated with a Cyclic Quiver and a Monic Polynomial

Abstract

In this article, we compute the Hochschild homology group of A = KΓ/(f(X ^s )), where KΓ is the path algebra of the cyclic quiver Γ with s vertices and s arrows over a commutative ring K, f(x) is a monic polynomial over K, and X is the sum of all arrows in KΓ. Moreover, we compute the cyclic homology group of A in the case f(x) = (x − a) ^m , where a ∈ K, so that we can determine the cyclic homology of A in general when K is an algebraically closed field.

Key Words:

• Cyclic homology
• Hochschild homology
• Spectral sequences

2010 Mathematics Subject Classification:

• Primary: 19D55
• Secondary: 16E40

Notes

Communicated by D. Zacharia.