Exterior Powers of Symmetric Bilinear Forms
نویسنده
چکیده
We study exterior powers of classes of symmetric bilinear forms in the WittGrothendieck ring of a field of characteristic not equal to 2, and derive their basic properties. The exterior powers are used to obtain annihilating polynomials for quadratic forms in the Witt ring. 1991 AMS Subject Classification: 11E04, 11E81
منابع مشابه
Symmetric Powers of Symmetric Bilinear Forms
We study symmetric powers of classes of symmetric bilinear forms in the Witt-Grothendieck ring of a field of characteristic not equal to 2, and derive their basic properties and compute their classical invariants. We relate these to earlier results on exterior powers of such forms. 1991 AMS Subject Classification: 11E04, 11E81
متن کاملTensor, Exterior and Symmetric Algebras
3 The Exterior Algebra 6 3.1 Dimension of the Exterior Powers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.2 Bilinear Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.3 Other Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.3.1 The determinant formula . . . . . . . . . . . . . . . . . . . . . . . . . ...
متن کاملMotivic Zeta Functions of Motives
LetM be a tensor category with coefficients in a fieldK of characteristic 0, that is, a K-linear pseudo-abelian symmetric monoidal category such that the tensor product ⊗ of M is bilinear. Then symmetric and exterior powers of an object M ∈ M make sense, by using appropriate projectors relative to the action of the symmetric groups on tensor powers of M . One may therefore introduce the zeta fu...
متن کاملExterior Powers
Let R be a commutative ring. Unless indicated otherwise, all modules are R-modules and all tensor products are taken over R, so we abbreviate ⊗R to ⊗. A bilinear function out of M1 × M2 turns into a linear function out of the tensor product M1 ⊗ M2. In a similar way, a multilinear function out of M1 × · · · ×Mk turns into a linear function out of the k-fold tensor product M1 ⊗ · · · ⊗Mk. We wil...
متن کاملWitt rings of quadratically presentable fields
This paper introduces an approach to the axiomatic theory of quadratic forms based on {tmem{presentable}} partially ordered sets, that is partially ordered sets subject to additional conditions which amount to a strong form of local presentability. It turns out that the classical notion of the Witt ring of symmetric bilinear forms over a field makes sense in the context of {tmem{quadratically p...
متن کامل