- In mathematics,
anticommutativity is a
specific property of some non-commutative
mathematical operations.
Swapping the
position of two
arguments of an...
- (−1)deg(x)deg(y)yx for all
nonzero homogeneous elements x and y (i.e. it is an
anticommutative algebra) and has the
further property that x2 = 0 (nilpotence) for...
-
degree one component)
always contains nilpotent elements. A Z-graded
anticommutative algebra with the
property that x2 = 0 for
every element x of odd grade...
- (even) or 1 (odd). Some
graded rings (or algebras) are
endowed with an
anticommutative structure. This
notion requires a
homomorphism of the
monoid of the...
- {\displaystyle [A,[B,C]]+[B,[C,A]]+[C,[A,B]]=0}
Relation (3) is
called anticommutativity,
while (4) is the
Jacobi identity. [ A , B C ] = [ A , B ] C + B [...
- is
anticommutative and not ****ociative. The
cross product also
satisfies the
Jacobi identity. Lie
algebras are
algebras satisfying anticommutativity and...
-
causal structure of the
theory by
imposing either commutativity or
anticommutativity between spacelike separated fields. They also
postulate the existence...
-
properties follow from the definition,
including the
following identities:
Anticommutativity: x × y = − y × x {\displaystyle \mathbf {x} \times \mathbf {y} =-\mathbf...
-
product a → × b → {\displaystyle {\vec {a}}\times {\vec {b}}} No No (
anticommutative)
quaternions R 4 {\displaystyle \mathbb {R} ^{4}}
Hamilton product...
-
commutator operation in a group. The
following identity follows from
anticommutativity and
Jacobi identity and
holds in
arbitrary Lie algebra: [ x , [ y...
