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.
Generalized metric $n$-Leibniz algebra, metric Lie algebra, generalized orthogonal representation, generalized orthogonal derivation, generalized orthogonal automorphism
TANG, RONG and SONG, LINA
"Generalized metric $n$-Leibniz algebras and generalized orthogonal representation of metric Lie algebras,"
Turkish Journal of Mathematics: Vol. 42:
6, Article 19.
Available at: https://journals.tubitak.gov.tr/math/vol42/iss6/19