The discriminant Pfister form of an algebra with involution of capacity four
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arXiv
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| Format: | Preprint |
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2020
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| author | Becher, Karim Johannes Grenier-Boley, Nicolas Tignol, Jean-Pierre |
| author_facet | Becher, Karim Johannes Grenier-Boley, Nicolas Tignol, Jean-Pierre |
| contents | To an orthogonal or unitary involution on a central simple algebra of degree 4, or to a symplectic involution on a central simple algebra of degree 8, we associate a Pfister form that characterises the decomposability of the algebra with involution. In this way we obtain a unified approach to known decomposability criteria for several cases, and a new result for symplectic involutions on degree $8$ algebras in characteristic 2. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2008_08953 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | The discriminant Pfister form of an algebra with involution of capacity four Becher, Karim Johannes Grenier-Boley, Nicolas Tignol, Jean-Pierre Rings and Algebras K-Theory and Homology 11E04, 11E81, 12G05, 16H05, 16R50, 16W10 To an orthogonal or unitary involution on a central simple algebra of degree 4, or to a symplectic involution on a central simple algebra of degree 8, we associate a Pfister form that characterises the decomposability of the algebra with involution. In this way we obtain a unified approach to known decomposability criteria for several cases, and a new result for symplectic involutions on degree $8$ algebras in characteristic 2. |
| title | The discriminant Pfister form of an algebra with involution of capacity four |
| topic | Rings and Algebras K-Theory and Homology 11E04, 11E81, 12G05, 16H05, 16R50, 16W10 |
| url | https://arxiv.org/abs/2008.08953 |