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On generalized Clifford algebraC (n)4 andGL q (2;C) quantum group

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Abstract

The non commuting matrix elements of matrices from quantum groupGL q (2;C) withq≡ω being then-th root of unity are given a representation as operators in Hilbert space with help ofC (n)4 generalized Clifford algebra generators appropriately tensored with unit 2×2 matrix infinitely many times. Specific properties of such a representation are presented. Relevance of generalized Pauli algebra to azimuthal quantization of angular momentum alà Lévy-Leblond [10] and to polar decomposition ofSU q (2;C) quantum algebra alà Chaichian and Ellinas [6] is also commented.

The case ofq∈C, |q|=1 may be treated parallely.

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Authors and Affiliations

  1. Institute of Informatics, Bialystok University, ul. Sosnowa 64, PL-15-887, Bialystok, Poland

    A. K. Kwaśniewski

  2. College of Applied Mathematics and Computer Science, Czysta 11, PL-15-463, Bialystok, Poland

    A. K. Kwaśniewski

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Kwaśniewski, A.K. On generalized Clifford algebraC (n)4 andGL q (2;C) quantum group. AACA 9, 249–260 (1999). https://doi.org/10.1007/BF03042380

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