Covariant connections on bicovariant differential calculus

Authors

Jyotishman Bhowmick, Indian Statistical Institute, Kolkata
Sugato Mukhopadhyay, Indian Statistical Institute, Kolkata

Article Type

Research Article

Publication Title

Journal of Algebra

Abstract

Given a bicovariant differential calculus (E,d) such that the braiding map is diagonalisable in a certain sense, the bimodule of two-tensors admits a direct sum decomposition into symmetric and anti-symmetric tensors. This is used to prove the existence of a bicovariant torsionless connection on E. Following Heckenberger and Schmüdgen, we study invariant metrics and the compatibility of covariant connections with such metrics. A sufficient condition for the existence and uniqueness of bicovariant Levi-Civita connections is derived. This condition is shown to hold for cocycle deformations of classical Lie groups.

First Page

198

Last Page

250

DOI

10.1016/j.jalgebra.2020.08.001

Publication Date

12-1-2020

Comments

Open Access, Green

Recommended Citation

Bhowmick, Jyotishman and Mukhopadhyay, Sugato, "Covariant connections on bicovariant differential calculus" (2020). Journal Articles. 46.
https://digitalcommons.isical.ac.in/journal-articles/46