Algebra Forms with
$$d^{N} = 0$$
on Quantum Plane. Generalized Clifford Algebra Approach |
| |
Authors: | Viktor Abramov |
| |
Institution: | (1) Institute of Pure Mathematics, University of Tartu, J. Liivi 2, 50409 Tartu, Estonia |
| |
Abstract: | We construct a q-analog of exterior calculus with a differential d satisfying d
N
= 0, where N ≥ 2 and q is a primitive Nth root of unity, on a noncommutative space and introduce a notion of a q-differential k-form. A noncommutative space we consider is a reduced quantum plane. Our construction of a q-analog of exterior calculus is based on a generalized Clifford algebra with four generators and on a graded q-differential algebra. We study the structure of the algebra of q-differential forms on a reduced quantum plane and show that the first order calculus induced by the differential d is a coordinate calculus. The explicit formulae for partial derivatives of this first order calculus are found. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|