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 | |
| 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
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 journal › Article
}
TY - JOUR
T1 - Bi-invariant and noninvariant metrics on Lie groups
AU - Ghanam, Ryad
AU - Hindeleh, F.
AU - Thompson, G.
PY - 2007
Y1 - 2007
N2 - 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)].
AB - 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)].
UR - http://www.scopus.com/inward/record.url?scp=36148991511&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=36148991511&partnerID=8YFLogxK
U2 - 10.1063/1.2793603
DO - 10.1063/1.2793603
M3 - Article
VL - 48
JO - Journal of Mathematical Physics
JF - Journal of Mathematical Physics
SN - 0022-2488
IS - 10
M1 - 102903
ER -