Iwasawa Decomposition for Lie Superalgebras
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866929466368851968 |
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| author | Sherman, Alexander |
| author_facet | Sherman, Alexander |
| contents | Let $\mathfrak{g}$ be a basic simple Lie superalgebra over an algebraically closed field of characteristic zero, and $θ$ an involution of $\mathfrak{g}$ preserving a nondegenerate invariant form. We prove that either $θ$ or $δ\circθ$ admits an Iwasawa decomposition, where $δ$ is the canonical grading automorphism $δ(x)=(-1)^{\overline{x}}x$. The proof uses the notion of generalized root systems as developed by Serganova, and follows from a more general result on centralizers of certain tori coming from semisimple automorphisms of the Lie superalgebra $\mathfrak{g}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2004_03095 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Iwasawa Decomposition for Lie Superalgebras Sherman, Alexander Representation Theory Let $\mathfrak{g}$ be a basic simple Lie superalgebra over an algebraically closed field of characteristic zero, and $θ$ an involution of $\mathfrak{g}$ preserving a nondegenerate invariant form. We prove that either $θ$ or $δ\circθ$ admits an Iwasawa decomposition, where $δ$ is the canonical grading automorphism $δ(x)=(-1)^{\overline{x}}x$. The proof uses the notion of generalized root systems as developed by Serganova, and follows from a more general result on centralizers of certain tori coming from semisimple automorphisms of the Lie superalgebra $\mathfrak{g}$. |
| title | Iwasawa Decomposition for Lie Superalgebras |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2004.03095 |