New techniques for calculation of Jordan-Kronecker invariants for Lie algebras and Lie algebra representations
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916394260496384 |
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| author | Kozlov, I. K. |
| author_facet | Kozlov, I. K. |
| contents | We introduce two novel techniques that simplify calculation of Jordan-Kronecker invariants for a Lie algebra $\mathfrak{g}$ and for a Lie algebra representation $ρ$. First, the stratification of matrix pencils under strict equivalence puts restrictions on the Jordan-Kronecker invariants. Second, we show that the Jordan-Kronecker invariants of a semi-direct sum $\mathfrak{g} \ltimes_ρ V$ are sometimes determined by the Jordan-Kronecker invariants of the dual Lie algebra representation $ρ^*$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_09535 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | New techniques for calculation of Jordan-Kronecker invariants for Lie algebras and Lie algebra representations Kozlov, I. K. Representation Theory We introduce two novel techniques that simplify calculation of Jordan-Kronecker invariants for a Lie algebra $\mathfrak{g}$ and for a Lie algebra representation $ρ$. First, the stratification of matrix pencils under strict equivalence puts restrictions on the Jordan-Kronecker invariants. Second, we show that the Jordan-Kronecker invariants of a semi-direct sum $\mathfrak{g} \ltimes_ρ V$ are sometimes determined by the Jordan-Kronecker invariants of the dual Lie algebra representation $ρ^*$. |
| title | New techniques for calculation of Jordan-Kronecker invariants for Lie algebras and Lie algebra representations |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2409.09535 |