Bi-invariant and noninvariant metrics on Lie groups

Ryad Ghanam; F. Hindeleh; G. Thompson

doi:10.1063/1.2793603

Bi-invariant and noninvariant metrics on Lie groups

Ryad Ghanam, F. Hindeleh, G. Thompson

Research output: Contribution to journal › Article

Abstract

A restricted version of the inverse problem of Lagrangian dynamics for the canonical linear connection on a Lie group is studied. Specifically for solvable Lie algebras of dimension up to and including six all algebras for which there is a compatible pseudo-Riemannian metric on the corresponding linear Lie group are found. Of the 19 such metrics four are bi-invariant. The Lie algebras are taken from tables compiled originally by Mubarakzyanov [Izv. Vyssh. Uchebn. Zaved., Mat. 4, 104-116 (1963)] and Morozov [Izv. Vyssh. Uchebn. Zaved., Mat. 4, 161-171 (1958)].

Original language	English
Article number	102903
Journal	Journal of Mathematical Physics
Volume	48
Issue number	10
DOIs	https://doi.org/10.1063/1.2793603
Publication status	Published - 2007
Externally published	Yes

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ASJC Scopus subject areas

Physics and Astronomy(all)
Statistical and Nonlinear Physics
Mathematical Physics

Cite this

Ghanam, R., Hindeleh, F., & Thompson, G. (2007). Bi-invariant and noninvariant metrics on Lie groups. Journal of Mathematical Physics, 48(10), [102903]. https://doi.org/10.1063/1.2793603

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10.1063/1.2793603