## Root graded Lie algebras and homology of their coordinates II

The nonassociative case

**Yun Gao**

(York University)

Root graded Lie algebras of type $A_2$ allow alternative algebras (like
octonions) as coordinates while root graded Lie algebras of type $A_1$
allow Jordan algebras as coordinates. In this talk, the Seligman construction
for the type $A_2$ Lie algebra and the Tits-Kantor-Koecher construction
for the type $A_1$ Lie algebra will be introduced. Then we determine their
universal central extensions.