## Abstract

We study the Hopf algebra structure and the highest weight representation of a multiparameter version of U_{q}gl(2). The Hopf algebra maps of this algebra are explicitly given. We show that the multiparameter universal R matrix can be constructed directly as a quantum double intertwiner without using Reshetikhin's twisting transformation. We find there are two types highest weight representations for this algebra: type a corresponds to the qeneric q and type b corresponds to the case that q is a root of unity. When applying the representation theory to the multi-parameter universal R matrix, both standard and nonstandard colored solutions of the Yang-Baxter equation are obtained.

Original language | English |
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Pages (from-to) | 6529-6543 |

Number of pages | 15 |

Journal | Journal of Mathematical Physics |

Volume | 41 |

Issue number | 9 |

DOIs | |

State | Published - Sep 2000 |