Quantum algebra deforming maps, Clebsch-Gordan coefficients, coproducts, R and U matrices

Thomas Curtright, G. I. Ghandour, C. K. Zachos

Research output: Contribution to journalArticle

41 Citations (Scopus)

Abstract

Quantum algebra deforming maps explicitly define comultiplications that differ from the usual noncocommutative coproducts. Mapinduced 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 twoparameter 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 spinchains are outlined.

Original languageEnglish (US)
Pages (from-to)676-688
Number of pages13
JournalJournal of Mathematical Physics
Volume32
Issue number3
DOIs
StatePublished - 1991

Fingerprint

Clebsch-Gordan coefficients
Coproducts
Quantum Algebra
algebra
Similarity Transformation
R-matrix
Coefficient
matrices
difference equations
products
bears
Partial Difference Equations
hierarchies
tensors
Tensor Product
operators
physics
Physics
Operator

Keywords

  • ALGEBRAS
  • CASIMIR OPERATORS
  • CLEBSCHGORDAN COEFFICIENTS
  • IRREDUCIBLE REPRESENTATIONS
  • MAPPING
  • QUANTUM MECHANICS
  • SU2 GROUPS
  • TRANSFORMATIONS

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Quantum algebra deforming maps, Clebsch-Gordan coefficients, coproducts, R and U matrices. / Curtright, Thomas; Ghandour, G. I.; Zachos, C. K.

In: Journal of Mathematical Physics, Vol. 32, No. 3, 1991, p. 676-688.

Research output: Contribution to journalArticle

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