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An Example of $Z_{N}$-Graded Noncommutative Differential Calculus

A. E. F. Djemai·H. Smail
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Abstract

In this work, we consider the algebra $M_{N}(C)$ of $N\times N$ 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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BibTeXRIS

A. E. F. Djemai, H. Smail. 1999-08-03. An Example of $Z_{N}$-Graded Noncommutative Differential Calculus. https://arxiv.org/abs/math-ph/9908005

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