Reductive homogeneous spaces of the compact Lie group G₂

2022/11/13 by Draper, Cristina, Palomo, Francisco J.
#Differential Geometry (math.DG) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2211.06997

Abstract

The first author defended her doctoral thesis Espacios homogéneos reductivos y álgebras no asociativas in 2001, supervised by P. Benito and A. Elduque. This thesis contained the classification of the Lie-Yamaguti algebras with standard enveloping algebra \mathfrakg₂ over fields of characteristic zero, which in particular gives the classification of the homogeneous reductive spaces of the compact Lie group G₂. In this work we revisit this classification from a more geometrical approach. We provide too geometric models of the corresponding homogeneous spaces and make explicit some relations among them.

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