back to author index
   
title:
 
On a graded q-differential algebra
publication:
 
JNMP
volume-issue:   13 - Supplement
pages:   1 - 8
ISSN:
  1402-9251
DOI:
  doi:10.2991/jnmp.2006.13.s.1 (how to use a DOI)
author(s):
 
Viktor ABRAMOV
publication date:
 
August 2006
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:
 
© The authors.
This article is distributed under the terms of the Creative Commons Attribution License 4.0, which permits non-commercial use, distribution and reproduction in any medium, provided the original work is properly cited. See for details: https://creativecommons.org/licenses/by-nc/4.0/
full text: