An introduction to universal central extensions of Lie
superalgebras
We provide an introduction to the theory of universal
central extensions of Lie superalgebras. In particular, we show that
a Lie superalgebra has a universal central extension if and only if it
is perfect. For perfect Lie superalgebras we provide a model for the
universal central extension, which is the super version of a
construction first given by van der Kallen for Lie algebras. It has the
advantage that it works for Lie superalgebras over commutative
superrings, which is the setting of the paper. Another topic
considered is the lifting of automorphisms and derivations to the
universal central extension.
(This paper has appeared in
``Groups, Rings, Lie and Hopf algebras'' (St. John's, NF, 2001),
Volume 555, pp. 141--166, Kluwer Acad. Publ., 2003)
E. Neher < neher@uottawa.ca >