Last Updated
：2025/12/06
Witt group
Noun
broadly
(algebra)
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;
Japanese Meaning
Witt群：特徴≠2の体 k 上の非退化対称双線形形式の同値類からなるアーベル群。ここで、同値類の定義は、各形式が代数的に metabolic (代数的二次空間を加える操作により相互に得られる) 形であるという関係に基づいており、群の演算は直交和（orthogonal direct sum）によって定義される。
Sense（1）
(algebra)
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;
Sense（2）
（ plural ）
Quizzes for review
(algebra) 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;
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See correct answer
Witt group
The classification of quadratic forms over a field often relies on computations in the Witt group.
See correct answer
The classification of quadratic forms over a field often relies on computations in the Witt group.
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English - English
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