I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2009, VOLUME 15, NUMBER 8, PAGES 3-93
On the structure of a relatively free Grassmann algebra
A. V. Grishin
L. M. Tsybulya
View as HTML
View as gif image
We investigate the multiplicative and T-space structure of the
relatively free algebra with
a unity corresponding to the identity
over an infinite field of characteristic
The highest emphasis is placed on unitary closed T-spaces over
a field of characteristic .
We construct a diagram containing all basic T-spaces of the
algebra , which form
infinite chains of the inclusions.
One of the main results is the decomposition of quotient T-spaces
connected with into
a direct sum of simple components.
Also, the studied T-spaces are commutative subalgebras
of ; thus, the
structure of and its
subalgebras can be described as modules over these commutative
Separately, we consider the specifics of the case .
In Appendix, we study nonunitary closed T-spaces and the case of
a field of zero characteristic.
Last modified: September 14, 2010