Witt group (English, noun)
expansion: Witt group (plural Witt groups)
Senses:
topics: algebra
mathematics
sciences
glosses: Given a field k of characteristic ≠ 2, the abelian group of equivalence classes of nondegenerate symmetric bilinear forms over k (where the equivalence relation is such that two forms are equivalent if each is obtainable from the other by adding a metabolic quadratic space), with the group operation corresponding to that of orthogonal direct sum of forms;
topics: algebra
algebraic-geometry
geometry
mathematics
sciences
glosses: Given a field k of characteristic ≠ 2, the abelian group of equivalence classes of nondegenerate symmetric bilinear forms over k (where the equivalence relation is such that two forms are equivalent if each is obtainable from the other by adding a metabolic quadratic space), with the group operation corresponding to that of orthogonal direct sum of forms;
(algebraic geometry, by extension) given a variety X, the quotient of the Grothendieck group of isometry classes of quadratic spaces on X, with respect to orthogonal sum, modulo the subgroup generated by metabolic spaces
(category theory, by extension) given a category with duality, the quotient of isometry classes of symmetric spaces, modulo metabolic spaces.
given a variety X, the quotient of the Grothendieck group of isometry classes of quadratic spaces on X, with respect to orthogonal sum, modulo the subgroup generated by metabolic spaces
tags: broadly
topics: algebra
category-theory
computing
engineering
mathematics
natural-sciences
physical-sciences
sciences
glosses: Given a field k of characteristic ≠ 2, the abelian group of equivalence classes of nondegenerate symmetric bilinear forms over k (where the equivalence relation is such that two forms are equivalent if each is obtainable from the other by adding a metabolic quadratic space), with the group operation corresponding to that of orthogonal direct sum of forms;
(algebraic geometry, by extension) given a variety X, the quotient of the Grothendieck group of isometry classes of quadratic spaces on X, with respect to orthogonal sum, modulo the subgroup generated by metabolic spaces
(category theory, by extension) given a category with duality, the quotient of isometry classes of symmetric spaces, modulo metabolic spaces.
given a category with duality, the quotient of isometry classes of symmetric spaces, modulo metabolic spaces.
tags: broadly
Forms:
form: Witt groups
tags: plural