Reductive homogeneous spaces of the compact Lie group $G_2$

Cristina Draper; Francisco J. Palomo

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arXiv · 2211.06997

Reductive homogeneous spaces of the compact Lie group $G_2$

Cristina Draper·Francisco J. Palomo

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Abstract

The first author defended her doctoral thesis Espacios homog\'eneos reductivos y \'algebras 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 $\mathfrak{g}_2$ over fields of characteristic zero, which in particular gives the classification of the homogeneous reductive spaces of the compact Lie group $G_2$. 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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BibTeX RIS

Cristina Draper, Francisco J. Palomo. 2022-11-13. Reductive homogeneous spaces of the compact Lie group $G_2$. https://arxiv.org/abs/2211.06997

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