The cyclic homology of monogenic extensions in the noncommutative setting

TL;DR

This paper investigates the Hochschild and cyclic homologies of noncommutative monogenic extensions, providing explicit computations for certain rank 1 Hopf algebras, thereby advancing understanding in noncommutative algebraic structures.

Contribution

It introduces methods to compute Hochschild and cyclic homologies for noncommutative monogenic extensions, including specific calculations for rank 1 Hopf algebras.

Findings

Computed Hochschild and cyclic homologies for specific rank 1 Hopf algebras

Developed techniques applicable to noncommutative monogenic extensions

Enhanced understanding of homological properties in noncommutative algebra

Abstract

We study the Hochschild and cyclic homologies of noncommutative monogenic extensions. As an aplication we compute the Hochschild and cyclic homologies of the rank~1 Hopf algebras introduced by L. Krop and D. Radford in [Finite dimensional Hopf algebras of rank 1 in characteristic 0, Journal of Algebra 302, no. 1, 214-230} (2006)].