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.