Quadratic algebras, Clifford algebras, and arithmetic Witt groups

zbMath0791.11021MaRDI QIDQ1312223

Alexander J. Hahn

Publication date: 18 January 1994

Published in: Universitext (Search for Journal in Brave)

zbMATH Keywords

quadratic formsPicard groupClifford algebrasClifford indexstandard modulesquadratic algebrasWitt groupscommutative ringsquadratic moduleClifford modulesexterior algebrasarithmetic Dedekind ringHasse domainspecial elementsArf algebradiscriminant modulesfree quadratic algebraslarge number of exercisesseparable quadratic algebras

Mathematics Subject Classification ID

Quadratic forms over general fields (11E04) Algebraic theory of quadratic forms; Witt groups and rings (11E81) Research exposition (monographs, survey articles) pertaining to number theory (11-02) Clifford algebras, spinors (15A66) Quadratic and bilinear forms, inner products (15A63) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05) Exterior algebra, Grassmann algebras (15A75) Quadratic spaces; Clifford algebras (11E88) Research exposition (monographs, survey articles) pertaining to commutative algebra (13-02) General commutative ring theory (13A99) Research exposition (monographs, survey articles) pertaining to linear algebra (15-02)

Related Items (18)

Counting non-isomorphic generalized Hamilton quaternions ⋮ Lie algebra of unit tangent bundle ⋮ Involutions in dual split-quaternions ⋮ Generalized quaternion rings over \(\mathbb {Z}/n\mathbb {Z}\) for an odd \(n\) ⋮ Discriminant algebras of finite rank algebras and quadratic trace modules ⋮ Unnamed Item ⋮ Products, coproducts, and singular value decomposition ⋮ Tensor products and discriminants of unital quadratic forms over commutative rings ⋮ On the structure of quaternion rings over \(\mathbb{Z}/n\mathbb{Z}\) ⋮ Mayer-vietoris sequences for the hermitian picard group ⋮ Witt groups of smooth projective quadrics ⋮ Smooth lattices over quadratic integers ⋮ Separable free quadratic algebras over quadratic integers ⋮ On factorizations of generically étale double coverings ⋮ Isotropic quadrangular algebras ⋮ A Gersten-Witt complex for hermitian Witt groups of coherent algebras over schemes II: Involution of the second kind ⋮ A characterization of quadratic forms of type \(E_6\), \(E_7\), and \(E_8\) ⋮ Limits of rank 4 Azumaya algebras and applications to desingularization.

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