特征 2 中低度卷积的维特不变式

Jean-Pierre Tignol
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引用次数: 0

摘要

在特征为 2 美元的域上,阶数为 8 美元的中央简单代数上的每一个交映内卷都典型地关联着一个 3 美元折叠和一个 5 美元折叠的二次普菲斯特形式。在阶数为 4 元的中心简单代数上的相同构造,将每一个单元卷积关联到一个 2 元对折和一个 4 元对折的菲斯特二次方形式,并将每一个正交卷积关联到一个 1 元对折和一个 3 元对折的准菲斯特形式。这些形式包含了有卷积的代数的结构信息。
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Invariants de Witt des involutions de bas degré en caractéristique 2
A $3$-fold and a $5$-fold quadratic Pfister forms are canonically associated to every symplectic involution on a central simple algebra of degree $8$ over a field of characteristic $2$. The same construction on central simple algebras of degree $4$ associates to every unitary involution a $2$-fold and a $4$-fold Pfister quadratic forms, and to every orthogonal involution a $1$-fold and a $3$-fold quasi-Pfister forms. These forms hold structural information on the algebra with involution.
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