The quantum double of the Yangian of the Lie superalgebra A(m, n) and computation of the universal R-matrix
| Autor: | V. A. Stukopin |
|---|---|
| Rok vydání: | 2007 |
| Předmět: |
Statistics and Probability
Pure mathematics Applied Mathematics General Mathematics Computation Mathematics::Rings and Algebras Lie superalgebra Superalgebra High Energy Physics::Theory Triangular decomposition Nonlinear Sciences::Exactly Solvable and Integrable Systems Mathematics::Quantum Algebra Pairing Yangian Mathematics::Representation Theory Quantum R-matrix Mathematics |
| Zdroj: | Journal of Mathematical Sciences. 142:1989-2006 |
| ISSN: | 1573-8795 1072-3374 |
| DOI: | 10.1007/s10958-007-0106-5 |
| Popis: | The Yangian double DY(A(m, n)) of the Lie superalgebra A(m, n) is described in terms of generators and defining relations. We prove the triangular decomposition for Yangian Y(A(m, n)) and its quantum double DY(A(m, n)) as a corollary of the PBW theorem. We introduce normally ordered bases in the Yangian and its dual Hopf superalgebra in the quantum double. We calculate the pairing formulas between the elements of these bases. We obtain the formula for the universal R-matrix of the Yangian double. The formula for the universal R-matrix of the Yangian, which was introduced by V. Drinfel’d, is also obtained. |
| Databáze: | OpenAIRE |
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