Bi-invariant and noninvariant metrics on Lie groups

Ryad Ghanam, F. Hindeleh, G. Thompson

Research output: Contribution to journalArticle

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 languageEnglish
Article number102903
JournalJournal of Mathematical Physics
Volume48
Issue number10
DOIs
Publication statusPublished - 2007
Externally publishedYes

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algebra
Solvable Lie Algebra
Linear Connection
Metric
Invariant
Linear Group
Riemannian Metric
Tables
Lie Algebra
Inverse Problem
Algebra

ASJC Scopus subject areas

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

Cite this

Bi-invariant and noninvariant metrics on Lie groups. / Ghanam, Ryad; Hindeleh, F.; Thompson, G.

In: Journal of Mathematical Physics, Vol. 48, No. 10, 102903, 2007.

Research output: Contribution to journalArticle

Ghanam, Ryad ; Hindeleh, F. ; Thompson, G. / Bi-invariant and noninvariant metrics on Lie groups. In: Journal of Mathematical Physics. 2007 ; Vol. 48, No. 10.
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