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Some Noncommutative Geometric Aspects of SU_q(2)

Debashish Goswami
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Abstract

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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Debashish Goswami. 2002-07-30. Some Noncommutative Geometric Aspects of SU_q(2). https://arxiv.org/abs/math-ph/0108003

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