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Some Noncommutative Geometric Aspects of SU_q(2) | | Debashish Goswami
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10 Aug 2001 | | Subject: | Mathematical Physics; Operator Algebras MSC-class: 81R50, 58B34, 81R60 | math-ph math.MP math.OA | | 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. | | Source: | arXiv, math-ph/0108003 | | Services: | Forum | Review | PDF | Favorites | |
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