title: 
On a graded qdifferential algebra 

publication: 

volumeissue:  13  Supplement  
pages:  1  8  
ISSN: 
14029251  
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 qdifferential algebra by means of a graded qcommutator, where q is a
primitive Nth root of unity. The Ndifferential d of the graded qdifferential algebra
is a homogeneous endomorphism of degree 1 satisfying the graded qLeibniz 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 Ndifferential of the
graded qdifferential algebra. Making use of the higher order differentials dk
x induced
by the Ndifferential d we construct an analogue of an algebra of differential forms
with exterior differential satisfying dN
= 0.


copyright: 
© The authors.
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