We investigate the existence of left-invariant closed G2-structures on seven-dimensional non-solvable Lie groups, providing the first examples of this type. When the Lie algebra has trivial Levi decomposition, we show that such a structure exists only when the semisimple part is isomorphic to sl(2,R) and the radical is unimodular and centerless. Moreover, we classify unimodular Lie algebras with non-trivial Levi decomposition admitting closed G2-structures.
Closed G_2-structures on non-solvable Lie groups
Anna Fino;Alberto Raffero
2019-01-01
Abstract
We investigate the existence of left-invariant closed G2-structures on seven-dimensional non-solvable Lie groups, providing the first examples of this type. When the Lie algebra has trivial Levi decomposition, we show that such a structure exists only when the semisimple part is isomorphic to sl(2,R) and the radical is unimodular and centerless. Moreover, we classify unimodular Lie algebras with non-trivial Levi decomposition admitting closed G2-structures.
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