Hodge Operators and Exceptional Isomorphisms between Unitary Groups
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866913542188302336 |
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| author | Kramer, Linus Stroppel, Markus J. |
| author_facet | Kramer, Linus Stroppel, Markus J. |
| contents | We give a generalization of the Hodge operator to spaces $(V,h)$ endowed with a hermitian or symmetric bilinear form $h$ over arbitrary fields, including the characteristic two case. Suitable exterior powers of $V$ become free modules over an algebra $K$ defined using such an operator. This leads to several exceptional homomorphisms from unitary groups (with respect to $h$) into groups of semi-similitudes with respect to a suitable form over some subfield of $K$. The algebra $K$ depends on $h$; it is a composition algebra unless $h$ is symmetric and the characteristic is two. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_11044 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Hodge Operators and Exceptional Isomorphisms between Unitary Groups Kramer, Linus Stroppel, Markus J. Group Theory 20G15 20E32 20G20 20G40 22C05 11E39 11E57 We give a generalization of the Hodge operator to spaces $(V,h)$ endowed with a hermitian or symmetric bilinear form $h$ over arbitrary fields, including the characteristic two case. Suitable exterior powers of $V$ become free modules over an algebra $K$ defined using such an operator. This leads to several exceptional homomorphisms from unitary groups (with respect to $h$) into groups of semi-similitudes with respect to a suitable form over some subfield of $K$. The algebra $K$ depends on $h$; it is a composition algebra unless $h$ is symmetric and the characteristic is two. |
| title | Hodge Operators and Exceptional Isomorphisms between Unitary Groups |
| topic | Group Theory 20G15 20E32 20G20 20G40 22C05 11E39 11E57 |
| url | https://arxiv.org/abs/2208.11044 |