Even Stiefel-Whitney invariants for anti-hermitian quaternionic forms
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arXiv
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866909380975263744 |
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| author | Garrel, Nicolas |
| author_facet | Garrel, Nicolas |
| contents | We extend all cohomological invariants of similarity classes of quadratic forms to anti-hermitian forms over a quaternion algebra. This uses the fact that such invariants can be lifted to Witt invariants, which can be described as combinations of $λ$-operations, and those $λ$-operations have recently been extended to hermitian forms over algebras with involution. In the article we present a detailed combinatoric description of invariants of quadratic forms which are partially diagonalized, and show how this combinatorics extend to anti-hermitian quaternionic forms. The methods developped here are intended to be later used for general algebras with involution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_07807 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Even Stiefel-Whitney invariants for anti-hermitian quaternionic forms Garrel, Nicolas K-Theory and Homology 11E81, 16W70, 12G05 We extend all cohomological invariants of similarity classes of quadratic forms to anti-hermitian forms over a quaternion algebra. This uses the fact that such invariants can be lifted to Witt invariants, which can be described as combinations of $λ$-operations, and those $λ$-operations have recently been extended to hermitian forms over algebras with involution. In the article we present a detailed combinatoric description of invariants of quadratic forms which are partially diagonalized, and show how this combinatorics extend to anti-hermitian quaternionic forms. The methods developped here are intended to be later used for general algebras with involution. |
| title | Even Stiefel-Whitney invariants for anti-hermitian quaternionic forms |
| topic | K-Theory and Homology 11E81, 16W70, 12G05 |
| url | https://arxiv.org/abs/2304.07807 |