Open AccessGeometric structures on Lie algebras and double extensions
Author(s) -
M. C. Rodríguez-Vallarte,
G. Salgado
Publication year - 2018
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/proc/14127
Subject(s) - symplectic geometry , lie algebra , pure mathematics , mathematics , invariant (physics) , algebra over a field , mathematical physics
Given a finite-dimensional real or complex Lie algebra g {\frak g} equipped with a geometric structure (i.e., either an invariant metric, a symplectic or contact structure), the aim of this work is to show that the double extension process introduced by V. Kac allows one to generate Lie algebras equipped with the same type of geometric structure. In particular, for an exact symplectic Lie algebra, through a double extension process it is possible to construct new exact symplectic Lie algebras.