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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.06045 |
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| _version_ | 1866911030748119040 |
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| author | Kunyavskii, Boris Makedonskyi, Ievgen Regeta, Andriy |
| author_facet | Kunyavskii, Boris Makedonskyi, Ievgen Regeta, Andriy |
| contents | The length of an element $z$ of a Lie algebra $L$ is defined as the smallest number $s$ needed to represent $z$ as a sum of $s$ brackets. The bracket width of $L$ is defined as supremum of the lengths of its elements. Given a finite-dimensional simple Lie algebra $\mathfrak g$ over an algebraically closed field $k$ of characteristic zero, we study the bracket width of current Lie algebras $L=\mathfrak g\otimes A$. We show that for an arbitrary $A$ the width is at most 2. For $A=k[[t]]$ and $A=k[t]$ we compute the width for algebras of types A and C. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06045 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bracket width of current Lie algebras Kunyavskii, Boris Makedonskyi, Ievgen Regeta, Andriy Rings and Algebras The length of an element $z$ of a Lie algebra $L$ is defined as the smallest number $s$ needed to represent $z$ as a sum of $s$ brackets. The bracket width of $L$ is defined as supremum of the lengths of its elements. Given a finite-dimensional simple Lie algebra $\mathfrak g$ over an algebraically closed field $k$ of characteristic zero, we study the bracket width of current Lie algebras $L=\mathfrak g\otimes A$. We show that for an arbitrary $A$ the width is at most 2. For $A=k[[t]]$ and $A=k[t]$ we compute the width for algebras of types A and C. |
| title | Bracket width of current Lie algebras |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2404.06045 |