THE UNIQUENESS THEOREM FOR THE UNIVERSAL R-MATRIX

被引：60

作者：

KHOROSHKIN, SM ^{[1
]}

TOLSTOY, VN ^{[1
]}

机构：

[1] MV LOMONOSOV STATE UNIV,INST NUCL PHYS,MOSCOW 119899,USSR

来源：

LETTERS IN MATHEMATICAL PHYSICS | 1992年 / 24卷 / 03期

关键词：

D O I：

10.1007/BF00402899

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Up to now, the universal R-matrix for quantized Kac-Moody algebras* is believed to be uniquely determined (for some ansatz) by properties of a quasi-cocommutativity and a quasi-triangularity. We prove here that the universal R-matrix (for the same ansatz) is uniquely determined by the property of the quasi-cocommutativity only. Thus, the quasi-triangular property (and the Yang-Baxter equation!) for the universal R-matrix is a consequence of the linear equation of the quasi-cocommutativity. The proof is based on properties of singular vectors in the tensor product of the Verma modules and the structure of extremal projector for quantized algebras. Explicit expressions of the universal R-matrix for quantized algebras U(q)(A1(1)) and U(q)(A2(2)) are given.

引用

页码：231 / 244

页数：14

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