On certain classes of Sp(2,R) symmetric G₂ structures

2019/08/13 by Paweł Nurowski, Nurowski, Paweł
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1908.04544

openalex publication_date 2019/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We find two different families of Sp(2,R) symmetric G₂ structures in seven dimensions. These are G₂ structures with G₂ being the split real form of the simple exceptional complex Lie group G₂. The first family has τ₂≡ 0, while the second family has τ₁≡τ₂≡ 0. The families are different in the sense that the first one lives on a homogoneous space Sp(2,R)/SL(2,R)_l, and the second one lives on a homogeneous space Sp(2,R)/Sl(2,R)_s. Here SL(2,R)_l is an SL(2,R) corresponding to the \mathfraksl(2,R) related to the long roots in the root diagram of \mathfraksp(2,R), and SL(2,R)_s is an SL(2,R) corresponding to the \mathfraksl(2,R) related to the short roots in the root diagram of \mathfraksp(2,R).

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