Last Updated
：2025/12/06
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 ）
Quizzes for review
(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).
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Clifford algebra
In my graduate seminar, we explored how a Clifford algebra can encode geometric reflections and rotations in arbitrary dimensions.
See correct answer
In my graduate seminar, we explored how a Clifford algebra can encode geometric reflections and rotations in arbitrary dimensions.
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