Generalized metric $n$-Leibniz algebras and generalized orthogonal representation of metric Lie algebras

Authors: RONG TANG, LINA SONG

Abstract: We introduce the notion of a generalized metric $n$-Leibniz algebra and show that there is a one-to-one correspondence between generalized metric $n$-Leibniz algebras and faithful generalized orthogonal representations of metric Lie algebras (called Lie triple datas). We further show that there is also a one-to-one correspondence between generalized orthogonal derivations (resp. generalized orthogonal automorphisms) on generalized metric $n$-Leibniz algebras and Lie triple data.

Keywords: Generalized metric $n$-Leibniz algebra, metric Lie algebra, generalized orthogonal representation, generalized orthogonal derivation, generalized orthogonal automorphism

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