Re: Lie supergroups

From: Very cryptic (very_cryptic_at_hotmail.com)
Date: 07/25/04 

Date: 25 Jul 2004 09:16:34 -0400

I'd like to clarify a couple of things. I know what a supermanifold is
(with the coordinates taking on values in a Grassman algebra) and I do
know one of the definitions of a Lie supergroup is a differentiable
supermanifold with a smooth (analytic) group structure. However, the
representations of such a supergroup act upon vector spaces over a
Grassman algebra. When I think of a Lie superalgebra, I think of a
real/complex Z_2 graded algebra with its representations acting upon
Z_2 graded real/complex vector spaces. I guess I should have been more
precise in my earlier question. What is the analog of the Lie group
for a real/complex Z_2 graded Lie superalgebra (not a Lie superalgebra
over a Grassman algebra)? The reason I'm asking this is because I'd
like the representations of such a Lie supergroup to act upon Z_2
graded real/complex vector spaces instead of a vector superspace.