Exterior form
From Encyclopedia of Mathematics
of degree , exterior
-form
A homogeneous element of degree of the exterior algebra
of a vector space
, i.e. an element of the
-th exterior power
. The expression "exterior form of degree r on the space V" usually denotes a skew-symmetric
-linear function (or a skew-symmetric
times covariant tensor) on
. The direct sum of the spaces of skew-symmetric
-linear functions on
,
endowed with the exterior product, is an algebra isomorphic to the exterior algebra
.
Under an exterior form one also understands a differential form.
How to Cite This Entry:
Exterior form. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Exterior_form&oldid=46888
Exterior form. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Exterior_form&oldid=46888
This article was adapted from an original article by A.L. Onishchik (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article