%0 Journal Article
%T Elliptic root systems of type $A_1$, a combinatorial study
%J Transactions on Combinatorics
%I University of Isfahan
%Z 2251-8657
%A Kharaghani, Zahra
%D 2019
%\ 12/01/2019
%V 8
%N 4
%P 11-21
%! Elliptic root systems of type $A_1$, a combinatorial study
%K Elliptic root systems
%K Elliptic Lie algebras
%K Jordan algebras
%R 10.22108/toc.2019.117338.1648
%X We consider some combinatorics of elliptic root systems of type $A_1$. 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.
%U https://toc.ui.ac.ir/article_24023_773c7ef2a4751d9ad0477a8e0cf7b337.pdf