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- Title
On certain classes of Sp(4,R) symmetric G2 structures.
- Authors
Nurowski, Paweł
- Abstract
We find two different families of Sp (4 , R) symmetric G 2 structures in seven dimensions. These are G 2 structures with G 2 being the split real form of the simple exceptional complex Lie group G 2 . The first family has τ 2 ≡ 0 , while the second family has τ 1 ≡ τ 2 ≡ 0 , where τ 1 , τ 2 are the celebrated G 2 -invariant parts of the intrinsic torsion of the G 2 structure. The families are different in the sense that the first one lives on a homogeneous space Sp (4 , R) / SL (2 , R) l , and the second one lives on a homogeneous space Sp (4 , R) / SL (2 , R) s . Here SL (2 , R) l is an SL (2 , R) corresponding to the sl (2 , R) related to the long roots in the root diagram of sp (4 , R) , and SL (2 , R) s is an SL (2 , R) corresponding to the sl (2 , R) related to the short roots in the root diagram of sp (4 , R) .
- Subjects
DYNKIN diagrams; HOMOGENEOUS spaces; LIE groups; TORSION
- Publication
Annals of Global Analysis & Geometry, 2021, Vol 59, Issue 2, p233
- ISSN
0232-704X
- Publication type
Article
- DOI
10.1007/s10455-020-09747-0