Yun Gao
(York University)
Central extensions of root graded Lie algebras can be characterized as certain homology of their coordinates. In this talk, I will focus on the simplest case: the elementary matrix Lie algebra $sl_n(R)$, where $R$ is an associative algebra. It turns out that the universal central extension of $sl_n(R)$ is the first Connes cyclic homology group of $R$ if $n>2$. Some variations of cyclic homology such as K\"ahler differentials, Hochschild homology and (skew) dihedral homology will also be introduced.