On a graded q-differential algebra

DOI

10.2991/jnmp.2006.13.s.1How to use a DOI?

Abstract

Given an associative unital ZN -graded algebra over the complex numbers we construct the graded q-differential algebra by means of a graded q-commutator, where q is a primitive N-th root of unity. The N-differential d of the graded q-differential algebra is a homogeneous endomorphism of degree 1 satisfying the graded q-Leibniz rule and dN = 0. We apply this construction to a reduced quantum plane and study the exterior calculus on a reduced quantum plane induced by the N-differential of the graded q-differential algebra. Making use of the higher order differentials dk x induced by the N-differential d we construct an analogue of an algebra of differential forms with exterior differential satisfying dN = 0.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Viktor Abramov
PY  - 2006
DA  - 2006/08/01
TI  - On a graded q-differential algebra
JO  - Journal of Nonlinear Mathematical Physics
SP  - 1
EP  - 8
VL  - 13
IS  - Supplement
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2006.13.s.1
DO  - 10.2991/jnmp.2006.13.s.1
ID  - Abramov2006
ER  -