L Šnobl and P Winternitz 2005 J. Phys. A: Math. Gen. 38 2687 doi:10.1088/0305-4470/38/12/011
A class of solvable Lie algebras and their Casimir invariants
L Šnobl1,2 and P Winternitz3
Show affiliationsA nilpotent Lie algebra 
with an (n − 1)-dimensional Abelian ideal is studied. All indecomposable solvable Lie algebras with 
as their nilradical are obtained. Their dimension is at most n + 2. The generalized Casimir invariants of 
and of its solvable extensions are calculated. For n = 4 these algebras figure in the Petrov classification of Einstein spaces. For larger values of n they can be used in a more general classification of Riemannian manifolds.
- PACS
- MSC
- Subjects
- Dates
-
Issue 12 (25 March 2005)
Received 4 November 2004, in final form 4 February 2005
Published 9 March 2005
-
A class of solvable Lie algebras and their Casimir invariants
L Šnobl and P Winternitz 2005 J. Phys. A: Math. Gen. 38 2687
-
Space missions to detect the cosmic gravitational-wave background
Neil J Cornish and Shane L Larson 2001 Class. Quantum Grav. 18 3473
-
Electron angular distributions after above-threshold multiphoton detachment of
by 1064 nm radiation
Dmitry Telnov and Shih-I Chu 1996 J. Phys. B: At. Mol. Opt. Phys. 29 4401
-
Sufficient conditions for the existence of bound states in a central potential
Fabian Brau 2004 J. Phys. A: Math. Gen. 37 6687
-
The LISA zero-signal solution
Massimo Tinto and Shane L Larson 2005 Class. Quantum Grav. 22 S531
-
Photoacoustic investigation of phase transitions in solids
T Somasundaram et al 1986 J. Phys. C: Solid State Phys. 19 2137
-
Reaction–diffusion pulses: a combustion model
Daniel Campos et al 2004 J. Phys. A: Math. Gen. 37 6609
-
Low temperature deposition of tantalum diffusion barrier by filtered cathodic vacuum arc
G Q Yu et al 2003 J. Phys. D: Appl. Phys. 36 1355
-
The cosmic dust aggregation experiment CODAG
Jürgen Blum et al 1999 Meas. Sci. Technol. 10 836
-
Quantum fractals in boxes
M V Berry 1996 J. Phys. A: Math. Gen. 29 6617
Users also read
What's this?Related review articles
What's this?- Theorems of Sylow type
- The effective temperature
- Independent functions and the geometry of Banach spaces