Subregular subalgebras and invariant generalized complex structures on Lie groups

2017/01/01 by Mayanskiy, Evgeny
#Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1701.00222

Abstract

We introduce the notion of a subregular subalgebra, which we believe is useful for classification of subalgebras of Lie algebras. We use it to construct a non-regular invariant generalized complex structure on a Lie group. As an illustration of the study of invariant generalized complex structures, we compute them all for the real forms of G2.

Related

• The subalgebras of G2
• Subalgebras of the rank two semisimple Lie algebras
• Subalgebras of Lie algebras. Example of sl(3,R) revisited
• Invariant and non-invariant almost complex structures on compact quotients of Lie groups
• Regular subalgebras and nilpotent orbits of real graded Lie algebras