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Remarks on the star product of functions on finite and compact groups |
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| Authors: | P. Aniello A. Ibort G. Marmo |
| Affiliation: | a Dipartimento di Scienze Fisiche dell'Università di Napoli ‘Federico II’ and Istituto Nazionale di Fisica Nucleare (INFN) — Sezione di Napoli, Complesso Universitario di Monte S. Angelo, via Cintia, 80126 Napoli, Italy b Facoltà di Scienze Biotecnologiche, Università di Napoli ‘Federico II’, Napoli, Italy c Departamento de Matemáticas, Universidad Carlos III de Madrid, 28911 Leganés, Madrid, Spain d P.N. Lebedev Physical Institute, Leninskii Prospect 53, Moscow 119991, Russia |
| Abstract: | We show that the characters  of irreducible unitary representations of finite groups and compact Lie groups provide kernels of star-product on complex valued functions f(g) of the group elements g. Examples of permutation groups of two and three elements as well as SU(2) group are considered. The k-deformed star products of the functions of finite and compact Lie groups are presented. The explicit form of the quantizers and dequantizers as well as the duality symmetry of the considered star products of the functions on the finite and compact Lie groups are discussed. |
| Keywords: | 03.65.-w 03.65.Wj |
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