English

On a graded q-differential algebra

Quantum Algebra 2015-06-26 v1 Differential Geometry

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.

Keywords

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