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The classification of quadratic forms over a field often relies on computations in the Witt group.
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The classification of quadratic forms over a field often relies on computations in the Witt group.
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Related words
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。
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