Journal of Nonlinear Mathematical Physics

Volume 13, Issue Supplement, August 2006, Pages 1 - 8

On a graded q-differential algebra

Authors
Viktor ABRAMOV
Corresponding Author
Viktor ABRAMOV
Available Online 1 August 2006.
DOI
https://doi.org/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.
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
13 - 100
Pages
1 - 8
Publication Date
2006/08
ISBN
91-974824-6-3
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.2006.13.s.1How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - Viktor ABRAMOV
PY  - 2006
DA  - 2006/08
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  - https://doi.org/10.2991/jnmp.2006.13.s.1
ID  - ABRAMOV2006
ER  -