Source Word
Clifford algebra
Noun
(algebra,
mathematical
physics)
A
unital
associative
algebra
which
generalizes
the
algebra
of
quaternions
but
which
is
not
necessarily
a
division
algebra;
it
is
generated
by
a
set
of
𝛾ᵢ
(with
i
ranging
from,
say,
1
to
n)
such
that
the
square
of
each
𝛾ᵢ
is
fixed
to
be
either
+1
or
−1,
depending
on
each
i,
and
such
that
any
product
𝛾ᵢ𝛾ⱼ
anticommutes
when
its
factors
are
distinct
(i.e.,
when
i
ne
j).
Japanese Meaning
クリフォード代数：単位元を持ち、結合則を満たす代数で、四元数代数を一般化したものです。各生成元γᵢの二乗が+1または-1に固定され、異なる生成元同士の積は反可換性を持つという性質があります。 / 数学および数学物理学で利用される構造。
Sense（1）
(algebra,
mathematical
physics)
A
unital
associative
algebra
which
generalizes
the
algebra
of
quaternions
but
which
is
not
necessarily
a
division
algebra;
it
is
generated
by
a
set
of
𝛾ᵢ
(with
i
ranging
from,
say,
1
to
n)
such
that
the
square
of
each
𝛾ᵢ
is
fixed
to
be
either
+1
or
−1,
depending
on
each
i,
and
such
that
any
product
𝛾ᵢ𝛾ⱼ
anticommutes
when
its
factors
are
distinct
(i.e.,
when
i
ne
j).
（ plural ）
