Turkish Journal of Mathematics
DOI
10.3906/mat-1803-61
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
First Page
3061
Last Page
3077
Recommended Citation
TANG, RONG and SONG, LINA
(2018)
"Generalized metric $n$-Leibniz algebras and generalized orthogonal representation of metric Lie algebras,"
Turkish Journal of Mathematics: Vol. 42:
No.
6, Article 19.
https://doi.org/10.3906/mat-1803-61
Available at:
https://journals.tubitak.gov.tr/math/vol42/iss6/19
