Fractional super Lie algebras and groups (Q2766170)
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scientific article; zbMATH DE number 1695625
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Fractional super Lie algebras and groups |
scientific article; zbMATH DE number 1695625 |
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27 January 2002
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fractional super Lie algebras
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fractional supergroups
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permutation groups
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Hopf algebra
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Fractional super Lie algebras and groups (English)
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In addition to the known fractional super Lie algebra (the \(n\)th root of a related Lie algebra or the \(S_n\)-graded algebra), based on the permutation group \(S_n\) invariant forms [\textit{M. Rausch de Traubenberg} and \textit{M. J. Slupinski}, J. Math. Phys. 41, 4556-4571 (2000; Zbl 0973.17038)], its dual, i.e. the corresponding fractional supergroup is introduced. In the paper both the fractional superalgebras and fractional supergroups are reformulated in the framework of the Hopf algebra formalism. As an example, a detailed description of \(S_2\)-graded \(\text{sl}(2)\) algebras is given.
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