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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Institution: | 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 algebraU
p, 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 standardU
p, q(gl(2)) corresponding to a nongeneric case. General finite dimensional coloured representation of the universal -matrix ofU
p, q(gl(2)) is also derived. This representation, in nongeneric cases, becomes a source for various (p, q)-dependent nonstandardR-matrices. Superization ofU
p, q(,H,X
±) leads to the super-Hopf algebraU
p, q(gl(1/1)). A contraction procedure then yields a (p, q)-deformed super-Heisenberg algebraU
p, q(sh(1)) and its universal -matrix. |
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Keywords: | |
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