Induced 3-Lie algebras, superalgebras and induced representations
We construct 3-Lie superalgebras on a commutative superalgebra by means of involution and even degree derivation. We construct a representation of induced 3-Lie algebras and superalgebras by means of a representation of initial (binary) Lie algebra, trace and supertrace. We show that the induced rep...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Estonian Academy Publishers
2020-04-01
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| Series: | Proceedings of the Estonian Academy of Sciences |
| Subjects: | |
| Online Access: | http://www.kirj.ee/public/proceedings_pdf/2020/issue_2/proc-2020-2-116-133.pdf |
| Summary: | We construct 3-Lie superalgebras on a commutative superalgebra by means of involution and even degree derivation. We construct a representation of induced 3-Lie algebras and superalgebras by means of a representation of initial (binary) Lie algebra, trace and supertrace. We show that the induced representation of 3-Lie algebra, that we constructed, is a representation by traceless matrices, that is, lies in the Lie algebra sl(V ), where V is a representation space. In the case of 2-dimensional representation we find conditions under which the induced representation of induced 3-Lie algebra is irreducible. We give the example of irreducible representation of induced 3-Lie algebra of 2nd order complex matrices. |
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| ISSN: | 1736-6046 1736-7530 |