3,396 research outputs found
Lie Bialgebras, Fields of Cohomological Dimension at Most 2 and Hilbert's Seventeenth Problem
We investigate Lie bialgebra structures on simple Lie algebras of non-split
type . It turns out that there are several classes of such Lie bialgebra
structures, and it is possible to classify some of them. The classification is
obtained using Belavin--Drinfeld cohomology sets, which are introduced in the
paper. Our description is particularly detailed over fields of cohomological
dimension at most two, and is related to quaternion algebras and the Brauer
group. We then extend the results to certain rational function fields over real
closed fields via Pfister's theory of quadratic forms and his solution to
Hilbert's Seventeenth Problem.Comment: The second version is a substantial augmentation of the first,
yielding a more complete picture. Comments are welcome
An Approach to Hopf Algebras via Frobenius Coordinates I
In Section 1 we introduce Frobenius coordinates in the general setting that
includes Hopf subalgebras. In Sections 2 and 3 we review briefly the theories
of Frobenius algebras and augmented Frobenius algebras with some new material
in Section 3. In Section 4 we study the Frobenius structure of an FH-algebra H
\cite{Par72} and extend two recent theorems in \cite{EG}. We obtain two Radford
formulas for the antipode in H and generalize in Section 7 the results on its
order in \cite{FMS}. We study the Frobenius structure on an FH-subalgebra pair
in Sections 5 and 6. In Section 8 we show that the quantum double of H is
symmetric and unimodular.Comment: 24 pages. To appear: Beitrage Alg. Geo
Classification of Lie bialgebras over current algebras
In the present paper we present a classification of Lie bialgebra structures
on Lie algebras of type g[[u]] and g[u], where g is a simple finite dimensional
Lie algebra.Comment: 26 page
Spherical principal series of quantum Harish-Chandra modules
The non-degenerate spherical principal series of quantum Harish-Chandra
modules is constructed. These modules appear in the theory of quantum bounded
symmertic domains.Comment: 14 page
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