An Example of Z_N-Graded Noncommutative Differential Calculus

1999/08/03 by A. E. F. Djemai, Djemai, A. E. F., H. Smail +1
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.math-ph/9908005

10 pages

arxiv created 1999/08/03 · arxiv updated 2009/11/30

Abstract

In this work, we consider the algebra M_N(C) of N× N matrices as a cyclic quantum plane. We also analyze the coaction of the quantum group \cal F and the action of its dual quantum algebra \cal H on it. Then, we study the decomposition of M_N(C) in terms of the quantum algebra representations. Finally, we develop the differential algebra of the cyclic group Z_N with d^N=0, and treat the particular case N=3.

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