Quantum Algebra Deforming Maps, Clebsch-gordan Coefficients, Coproducts, U and R Matrices
Mar, 1990
17 pages
Published in:
- J.Math.Phys. 32 (1991) 676-688
DOI:
Report number:
- IASSNS-HEP-90-26,
- ANL-HEP-PR-90-08,
- MIAMI-TH-1-90
Citations per year
Abstract: (AIP)
Quantum algebra deforming maps explicitly define comultiplications that differ from the usual noncocommutative coproducts. Map‐induced coproducts are connected to the usual ones by similarity transformations U that may be expressed either in terms of Clebsch–Gordan coefficients, or in a universal operator form. The product of two such U matrices yields the R matrix for a fixed value of the spectral parameter, which bears on the Yang–Baxterization of U as well as R. All this is explicitly illustrated for the tensor product 1/2⊗j of SU(2) q using several deforming maps whose coproducts are continuously connected by similarity transformations to form a two‐parameter manifold. Some observations are made on the general structure of U and R matrices, and of coproduct manifolds, based on the solutions of hierarchies of partial difference equations. Applications of deforming maps and U matrices to the physics of spin‐chains are outlined.- quantum group: SU(2)
- Clebsch-Gordan coefficients
- R-matrix
- algebra: Yang-Baxter
References(22)
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