On the quantum structure of the universal enveloping algebra of the Lie algebra \(\mathcal{ST}(2)\) (Q2762345)
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scientific article; zbMATH DE number 1687707
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the quantum structure of the universal enveloping algebra of the Lie algebra \(\mathcal{ST}(2)\) |
scientific article; zbMATH DE number 1687707 |
Statements
9 December 2002
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Lie bialgebras
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Hopf algebras
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Poisson brackets
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On the quantum structure of the universal enveloping algebra of the Lie algebra \(\mathcal{ST}(2)\) (English)
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Let \(ST(2)\) be the Lie group of upper triangular \(2 \times 2\) matrices with determinant \(1\), and let \(\mathcal{ST} (2)\) be the corresponding Lie algebra. A Lie bialgebra structure (respectively, a co-Poisson-Hopf algebra structure) is built in \(\mathcal{ST} (2)\) (resp., in the universal enveloping algebra \(\mathcal U(\mathcal{ST} (2))\)), with the help of a solution of the classical Yang-Baxter equation as considered by the author in [Lect. Mat. 18, 23-41 (1997; Zbl 0918.17008)]. This induces a one parameter deformation \(\mathcal U_h (\mathcal{ST} (2))\) of \(\mathcal U(\mathcal{ST} (2))\).
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