Geometry of the reduced quantum plane

Details Geometry of the reduced quantum plane Geometry of the reduced quantum plane

1998-11-19

arxiv.org/abs/math-ph/9811017v1

"Quantum Groups and Fundamental Physical Applications", D. Kastler, M. Rosso and T. Schucker, Eds.; Nova Science Publishers, 1

Physics

Mathematical Physics

17 pages, no figures, LaTeX, uses diagrams macro (included). Contribution to the proceedings of the conference "Quantum Groups

Scientific paper

We consider the space M of NxN matrices as a reduced quantum plane and discuss its geometry under the action and coaction of finite dimensional quantum groups (a quotient of U_q(SL(2)), q being an N-th root of unity, and its dual). We also introduce a differential calculus for M: a quotient of the Wess Zumino complex. We shall restrict ourselves to the case N odd and often choose the particular value N=3. The present paper (to appear in the proceedings of the conference "Quantum Groups and Fundamental Physical Applications", Palerme, December 1997) is essentially a short version of math-ph/9807012.

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