Differential Geometry on Linear Quantum Groups

TL;DR

This paper develops differential geometric tools such as exterior derivatives and Lie derivatives on the quantum group GL_q(N), and extends these constructions to SL_q(N) by imposing determinant unity, enriching quantum group calculus.

Contribution

Introduces differential geometric operators on quantum groups and constructs calculus on SL_q(N) from GL_q(N).

Findings

Defined exterior derivative, inner derivation, and Lie derivative on GL_q(N)

Constructed calculus on SL_q(N) from GL_q(N)

Extended quantum group calculus to special linear quantum groups

Abstract

An exterior derivative, inner derivation, and Lie derivative are introduced on the quantum group $GL_{q}(N)$. $SL_{q}(N)$ is then found by constructing matrices with determinant unity, and the induced calculus is found.