TY - JOUR
ID - 24023
TI - Elliptic root systems of type $A_1$, a combinatorial study
JO - Transactions on Combinatorics
JA - TOC
LA - en
SN - 2251-8657
AU - Kharaghani, Zahra
AD - Department of mathematics, University of Isfahan, Isfahan, Iran
Y1 - 2019
PY - 2019
VL - 8
IS - 4
SP - 11
EP - 21
KW - Elliptic root systems
KW - Elliptic Lie algebras
KW - Jordan algebras
DO - 10.22108/toc.2019.117338.1648
N2 - 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.
UR - https://toc.ui.ac.ir/article_24023.html
L1 - https://toc.ui.ac.ir/article_24023_773c7ef2a4751d9ad0477a8e0cf7b337.pdf
ER -