3 research outputs found
Lie bialgebras of generalized Witt type
In a paper by Michaelis a class of infinite-dimensional Lie bialgebras
containing the Virasoro algebra was presented. This type of Lie bialgebras was
classified by Ng and Taft. In this paper, all Lie bialgebra structures on the
Lie algebras of generalized Witt type are classified. It is proved that, for
any Lie algebra of generalized Witt type, all Lie bialgebras on are
coboundary triangular Lie bialgebras. As a by-product, it is also proved that
the first cohomology group is trivial.Comment: 14 page
Extensions of superalgebras of Krichever-Novikov type
An explicit construction of central extensions of Lie superalgebras of
Krichever-Novikov type is given. In the case of Jordan superalgebras related to
the superalgebras of Krichever-Novikov type we calculate a 1-cocycle with
coefficients in the dual space