Bi-invariant and noninvariant metrics on Lie groups

Ryad Ghanam, F. Hindeleh, G. Thompson

Research output: Contribution to journalArticle


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
Issue number10
Publication statusPublished - 2007
Externally publishedYes


ASJC Scopus subject areas

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

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