A note on $2$-plectic vector spaces
| Autor: | Mohammad Shafiee |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Journal of Mahani Mathematical Research, Vol 13, Iss 1, Pp 443-455 (2023) |
| Druh dokumentu: | article |
| ISSN: | 2251-7952 2645-4505 |
| DOI: | 10.22103/jmmr.2023.20889.1389 |
| Popis: | Among the $2$-plectic structures on vector spaces, the canonical ones and the $2$-plectic structures induced by the Killing form on semisimple Lie algebras are more interesting. In this note, we show that the group of linear preservers of the canonical $2$-plectic structure is noncompact and disconnected and its dimension is computed. Also, we show that the group of automorphisms of a compact semisimple Lie algebra preserving its $2$-plectic structure, is compact. Furthermore, it is shown that the $2$-plectic structure on a semisimple Lie algebra $\mathfrak{g}$ is canonical if and only if it has an abelian Lie subalgebra whose dimension satisfies in a special condition. As a consequence, we conclude that the $2$-plectic structures induced by the Killing form on some important classical Lie algebras are not canonical. |
| Databáze: | Directory of Open Access Journals |
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