Covariant q-Differential Calculus and its Deformations at q^N=1
Quantum Algebra
2007-05-23 v1 Differential Geometry
Abstract
We construct the generalized version of covariant Z_3-graded differential calculus introduced by one of us (R.K.), and then extended to the case of arbitrary Z_N grading. Here our main purpose is to establish the recurrence formulae for the N-th power of covariant q-differential D_q = d_q + A and to analyze more closely the particular case of q being an Nth primitive root of unity. The generalized notions of connection and curvature are introduced and several examples of realization are displayed for N=3 and N=4. Finally we briefly discuss the idea of infinitesimal deformations of the parameter q in the complex plane.
Keywords
Cite
@article{arxiv.math/0004165,
title = {Covariant q-Differential Calculus and its Deformations at q^N=1},
author = {R. Kerner and B. Niemeyer},
journal= {arXiv preprint arXiv:math/0004165},
year = {2007}
}
Comments
16 pages, no figures