On a graded q-differential algebra
Abstract
Given a unital associatve graded algebra 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-th power (N>1) of the differential of this graded q-differential algebra is equal to zero. We use our approach to construct the graded q-differential algebra in the case of a reduced quantum plane which can be endowed with a structure of a graded algebra. We consider the differential d satisfying d to power N equals zero as an analog of an exterior differential and study the first order differential calculus induced by this differential.
Cite
@article{arxiv.math/0509481,
title = {On a graded q-differential algebra},
author = {V. Abramov},
journal= {arXiv preprint arXiv:math/0509481},
year = {2015}
}
Comments
6 pages, submitted to the Proceedings of the "International Conference on High Energy and Mathematical Physics", Morocco, Marrakech, April 2005