Abstract

In this talk, we will discuss the universal central extensions of two families of matrix Lie superalgebras coordinatized by associative superalgebras with superinvolution, namely, generalized periplectic Lie superalgebras and generalized orthosymplectic Lie superalgebras. The key ingredient is that the second homology group of a generalized periplectic (resp. orthosymplectic) Lie superalgebra is identified with the -graded dihedral (resp. skew-dihedral) homology group of its coordinates superalgebra in most cases. We will also discuss the universal central extensions of a few matrix Lie superalgebras (usually involving matrices of small dimension) on which the identifications above fail.

The talk is based on the joint work with Zhihua Chang.