Volume 13, Issue Supplement, August 2006, Pages 1 - 8
On a graded q-differential algebra
Available Online 1 August 2006.
- https://doi.org/10.2991/jnmp.2006.13.s.1How to use a DOI?
- 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.
- 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 -