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| Paper IPM / Physic / 6485 |
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| Abstract: | |
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It is shown that the finite dimensional ireducible 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 3-dimensional torus S1 ×S1 ×S1 ( which may be thought of as a generalization of the cyclic representation ) to a 3-dimensional cube [ 0 , 1 ]×[ 0 , 1 ]×[ 0 , 1 ] .
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