Turkish Journal of Mathematics
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.
DOI
10.3906/mat-1803-61
Keywords
Generalized metric $n$-Leibniz algebra, metric Lie algebra, generalized orthogonal representation, generalized orthogonal derivation, generalized orthogonal automorphism
First Page
3061
Last Page
3077
Recommended Citation
TANG, R, & SONG, L (2018). Generalized metric $n$-Leibniz algebras and generalized orthogonal representation of metric Lie algebras. Turkish Journal of Mathematics 42 (6): 3061-3077. https://doi.org/10.3906/mat-1803-61
