Covariant q-Differential Calculus and its Deformations at q^N=1

2000/04/26 by R. Kerner, B. Niemeyer
Mathematics · #math.QA #math.DG #msc:53-XX #msc:15-XX #msc:81-XX

paper · pdf

published as Lett. Math. Phys., 45 (1998) 161-176 · 16 pages, no figures

arxiv created 2000/04/26 · arxiv updated 2009/11/30

Abstract

We construct the generalized version of covariant Z₃-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.

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