On the cyclic homology of certain universal differential graded algebras

TL;DR

This paper computes the periodic, cyclic, and negative cyclic homologies of a universal differential graded algebra obtained by killing a prime p in a p-torsion-free algebra, revealing detailed homological structures.

Contribution

It provides explicit calculations of cyclic homologies for the universal algebra formed by killing a prime in a p-torsion-free algebra, a novel contribution in this context.

Findings

Computed periodic cyclic homology of R//p over R.

Determined cyclic and negative cyclic homologies in infinitely many degrees.

Extended understanding of homological properties of universal differential graded algebras.

Abstract

Let $p$ be an odd prime and $R$ a $p$-torsion-free commutative $\mathbb{Z}_{(p)}$-algebra. We compute the periodic cyclic homology over $R$ of the universal differential graded algebra $R//p$ which is obtained from $R$ by universally killing $p$. We furthermore compute the cyclic and negative cyclic homologies of $R//p$ over $R$ in infinitely many degrees.