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Alternating algebra
In
mathematics
, an
alternating
algebra
is a -graded algebra for which for all
nonzero
homogeneous
elements
and and has the further
property
that for every
homogeneous element
of
odd degree
.
Examples
The
differential forms
on a
differentiable manifold
form an alternating algebra.
The
exterior algebra
is an alternating algebra.
The
cohomology ring
of a
topological space
is an alternating algebra.
Properties
The algebra formed as the
direct sum
of the homogeneous subspaces of
even degree
of an
anticommutative algebra
is a
subalgebra
contained in the
centre
of, and is thus
commutative
.
An
anticommutative
algebra over a
base
ring
in which 2 is not a
zero divisor
is alternating.
