Homology of quantum linear groups

TL;DR

This paper computes the Hochschild homology of quantum linear groups and monoids, specifically $M_q(n)$, $GL_q(n)$, and $SL_q(n)$, with coefficients derived from a modular pair in involution, advancing understanding of their algebraic structures.

Contribution

It provides explicit calculations of Hochschild homology for quantum linear groups and monoids, a novel contribution to quantum algebra and homological methods.

Findings

Hochschild homology of $M_q(n)$, $GL_q(n)$, and $SL_q(n)$ calculated

Results depend on coefficients from a modular pair in involution

Enhances understanding of quantum group algebraic properties

Abstract

For every $n\geq 1$, we calculate the Hochschild homology of the quantum monoids $M_q(n)$, and the quantum groups $GL_q(n)$ and $SL_q(n)$ with coefficients in a 1-dimensional module coming from a modular pair in involution.