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- W2783114952 abstract "In this paper, we study the relations between left-invariant flat connections on Lie groups, left-symmetric algebras, symplective Lie algebras, Frobenius Lie algebras and cuspidal prehomogeneous vector spaces. More specifically, we establish a one-to-one correspondence between left-symmetric Lie algebras with a right identity and cuspidal prehomogeneous vector spaces of a Lie group. As an application of our approach, we study the classification of the reduced cuspidal prehomogeneous vector spaces (G,r{ho},V) where G is a reductive Lie group. Fortunately, we prove that any of the left-symmetric structure on a reductive Lie algebra has a right identity. Then to give the complete classification of left-symmetric structure on reductive Lie algebras, we just need to give the classification of cuspidal prehomogeneous vector spaces for reductive Lie groups." @default.
- W2783114952 created "2018-01-26" @default.
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- W2783114952 date "2018-01-09" @default.
- W2783114952 modified "2023-09-27" @default.
- W2783114952 title "Cuspidal prehomogeneous vector spaces for reductive Lie groups and related algebraic and geometric structures" @default.
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