On a nonstandard two-parametric quantum algebra and its connections withU p,q (gl(2)) andU p,q(gl(1/1)) |
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Authors: | R. Chakrabarti R. Jagannathan |
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Affiliation: | 1. Department of Theoretical Physics, University of Madras, Guindy Campus, 600025, Madras, India 2. Institute of Mathematical Sciences, C I T Campus, Tharamani, 600113, Madras, India
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Abstract: | A quantum algebraUp, q (,H,X±) associated with a nonstandardR-matrix with two deformation parameters (p, q) is studied and, in particular, its universal -matrix is derived using Reshetikhin's method. Explicit construction of the (p, q)-dependent nonstandardR-matrix is obtained through a coloured generalized boson realization of the universal -matrix of the standardUp, q(gl(2)) corresponding to a nongeneric case. General finite dimensional coloured representation of the universal -matrix ofUp, q(gl(2)) is also derived. This representation, in nongeneric cases, becomes a source for various (p, q)-dependent nonstandardR-matrices. Superization ofUp, q(,H,X±) leads to the super-Hopf algebraUp, q(gl(1/1)). A contraction procedure then yields a (p, q)-deformed super-Heisenberg algebraUp, q(sh(1)) and its universal -matrix. |
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