Twisting of affine algebraic groups, II

Abstract: We use cite{G} to study the algebra structure of twisted cotriangular Hopf algebras

_{J} m a t h c a l O (G)_{J}

, where

J

is a Hopf

2

-cocycle for a connected nilpotent algebraic group

G

over

m a t h b b C

. In particular, we show that

_{J} m a t h c a l O (G)_{J}

is an affine Noetherian domain with Gelfand-Kirillov dimension

d i m (G)

, and that if

G

is unipotent and

J

is supported on

G

, then

_{J} m a t h c a l O (G)_{J} c o n g U (g)

as algebras, where

g = m L i e (G)

. We also determine the finite dimensional irreducible representations of

_{J} m a t h c a l O (G)_{J}

, by analyzing twisted function algebras on

(H, H)

-double cosets of the support

H s u b s e t G

of

J

. Finally, we work out several examples to illustrate our results.

Recommendations

This page was built for publication: Twisting of affine algebraic groups, II