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“School of Physic”

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Paper   IPM / Physic / 6486
School of Physics
  Title:   Representations of the Quantum Matrix Algebra Mq,p(2)
  Author(s):  V. Karimipour
  Status:   Published
  Journal: J. Phys. A: Math. Gen.
  No.:  28
  Vol.:  26
  Year:  1993
  Pages:   6277-6284
  Supported by:  IPM
  Abstract:
It is shown that finite-dimensional irreducible representations of the quantum matrix algebra Mq(3) (the coordinate ring of GLq(3)) exist only when q is a root of unity (qp=1). The dimensions of these representations can only be one of the following values: p3, p3/2, p3/4, or p3/8. The topology of the space of states ranges between two extremes, from a three-dimensional torus S1 ×S1 ×S1 (which may be thought of as a generalization of the cyclic representation) to a three-dimensional cube [0,1]×[0,1] ×[0,1].

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