Zahra Kharaghani - Department of mathematics, University of Isfahan, Isfahan, Iran

We consider some combinatorics of elliptic root systems of type $A_۱$. In particular, with respect to a fixed reflectable base, we give a precise description of the positive roots in terms of a ``positivity'' theorem. Also the set of reduced words of the corresponding Weyl group is precisely described. These then lead to a new characterization of the core of the corresponding Lie algebra, namely we show that the core is generated by positive root spaces.

Elliptic root systems, Elliptic Lie algebras, Jordan algebras