Homology, Homotopy and Applications

Volume 23 (2021)

Number 2

Homology of quantum linear groups

Pages: 9 – 31

DOI: https://dx.doi.org/10.4310/HHA.2021.v23.n2.a2

Authors

A. Kaygun (Istanbul Technical University, Istanbul, Turkey)

S. Sütlü (Işık University, Istanbul, Turkey)

Abstract

For every $n \geqslant 1$, 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.

Keywords

quantum groups, Hochschild homology

2010 Mathematics Subject Classification

16E40, 17B37, 20G42

Received 5 March 2020

Received revised 31 August 2020

Accepted 29 September 2020

Published 24 March 2021