TY - JOUR
T1 - Distinguished sets of semi-simple Lie algebras
AU - Chen, Xudong
AU - Gharesifard, Bahman
N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2021/11
Y1 - 2021/11
N2 - We call a finite, spanning set of a semi-simple real Lie algebra a distinguished set if it satisfies the following property: The Lie bracket of any two elements out of the set is, up to some constant, another element in the set; conversely, for any element in the set, there are two elements out of the set whose Lie bracket is, up to some constant, the given element. We show that every semi-simple real Lie algebra has a distinguished set.
AB - We call a finite, spanning set of a semi-simple real Lie algebra a distinguished set if it satisfies the following property: The Lie bracket of any two elements out of the set is, up to some constant, another element in the set; conversely, for any element in the set, there are two elements out of the set whose Lie bracket is, up to some constant, the given element. We show that every semi-simple real Lie algebra has a distinguished set.
KW - Real forms
KW - Root systems
KW - Simple Lie algebras
KW - Structure theory
UR - https://www.scopus.com/pages/publications/85103179416
U2 - 10.1007/s10801-021-01027-9
DO - 10.1007/s10801-021-01027-9
M3 - Article
AN - SCOPUS:85103179416
SN - 0925-9899
VL - 54
SP - 879
EP - 891
JO - Journal of Algebraic Combinatorics
JF - Journal of Algebraic Combinatorics
IS - 3
ER -