Open AccessLie algebras whose Lie groups have negative sectional curvature
Author(s) -
G. Salgado
Publication year - 2022
Publication title -
integración/revista integración, temas de matemáticas
Language(s) - English
Resource type - Journals
eISSN - 2145-8472
pISSN - 0120-419X
DOI - 10.18273/revint.v40n1-2022005
Subject(s) - mathematics , killing form , pure mathematics , adjoint representation of a lie algebra , lie conformal algebra , simple lie group , representation of a lie group , lie algebra , subalgebra , lie theory , adjoint representation , graded lie algebra , algebra over a field
The aim of this work is to completely describe two families of Lie algebras whose Lie groups have negative sectional curvature. The first family consists of Lie algebras satisfying the following property: given any two vectors in the Lie algebra, the linear subspace spanned by them is a Lie subalgebra. On the other hand, the second family consists of reduced Lie algebras of Iwasawa type.