Weak Lie symmetry and extended Lie algebra

Journal Article · Mon Apr 15 00:00:00 EDT 2013 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4795839· OSTI ID:22162865

Goenner, Hubert ^[1]

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1. Institute for Theoretical Physics, Friedrich-Hund-Platz 1, University of Goettingen, D-37077 Gottingen (Germany)

The concept of weak Lie motion (weak Lie symmetry) is introduced. Applications given exhibit a reduction of the usual symmetry, e.g., in the case of the rotation group. In this context, a particular generalization of Lie algebras is found ('extended Lie algebras') which turns out to be an involutive distribution or a simple example for a tangent Lie algebroid. Riemannian and Lorentz metrics can be introduced on such an algebroid through an extended Cartan-Killing form. Transformation groups from non-relativistic mechanics and quantum mechanics lead to such tangent Lie algebroids and to Lorentz geometries constructed on them (1-dimensional gravitational fields).

• OSTI ID: 22162865
• Journal Information: Journal of Mathematical Physics, Vol. 54, Issue 4; Other Information: (c) 2013 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
DISTRIBUTION
GRAVITATIONAL FIELDS
LIE GROUPS
METRICS
ONE-DIMENSIONAL CALCULATIONS
QUANTUM MECHANICS
REDUCTION
RELATIVISTIC RANGE
ROTATION
TRANSFORMATIONS