### 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 language | English (US) |
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Pages (from-to) | 676-688 |

Number of pages | 13 |

Journal | Journal of Mathematical Physics |

Volume | 32 |

Issue number | 3 |

DOIs | |

State | Published - Mar 1991 |

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### 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

*Journal of Mathematical Physics*,

*32*(3), 676-688. https://doi.org/10.1063/1.529410