Some Noncommutative Geometric Aspects of SU_q(2)

Details Some Noncommutative Geometric Aspects of SU_q(2) Some Noncommutative Geometric Aspects of SU_q(2)

2001-08-10

arxiv.org/abs/math-ph/0108003v4

Physics

Mathematical Physics

This is a revised and condensed version of the paper following the suggestions of the referee(s), and in this form it is conce

Scientific paper

We study various noncommutative geometric aspects of the compact quantum group SU_q(2) for positive q (not equal to 1), following the suggestion of Connes and his coauthors [CL, CD] for considering the so-called true Dirac operator. However, it turns out that the method of the above references do not extend to the case of positive (not equal to 1) values of q in the sense that the true Dirac operator does not have bounded commutators with "smooth" algebra elements in this case, in contrast to what happens for complex q of modulus 1. Nevertheless, we show how to obtain the canonical volume form, i.e. the Haar state, using the true Dirac operator.

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