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Title: Weak Lie symmetry and extended Lie algebra

Abstract

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).

Authors:
 [1]
  1. Institute for Theoretical Physics, Friedrich-Hund-Platz 1, University of Goettingen, D-37077 Gottingen (Germany)
Publication Date:
OSTI Identifier:
22162865
Resource Type:
Journal Article
Journal Name:
Journal of Mathematical Physics
Additional Journal Information:
Journal Volume: 54; Journal Issue: 4; Other Information: (c) 2013 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0022-2488
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; DISTRIBUTION; GRAVITATIONAL FIELDS; LIE GROUPS; METRICS; ONE-DIMENSIONAL CALCULATIONS; QUANTUM MECHANICS; REDUCTION; RELATIVISTIC RANGE; ROTATION; TRANSFORMATIONS

Citation Formats

Goenner, Hubert. Weak Lie symmetry and extended Lie algebra. United States: N. p., 2013. Web. doi:10.1063/1.4795839.
Goenner, Hubert. Weak Lie symmetry and extended Lie algebra. United States. https://doi.org/10.1063/1.4795839
Goenner, Hubert. 2013. "Weak Lie symmetry and extended Lie algebra". United States. https://doi.org/10.1063/1.4795839.
@article{osti_22162865,
title = {Weak Lie symmetry and extended Lie algebra},
author = {Goenner, Hubert},
abstractNote = {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).},
doi = {10.1063/1.4795839},
url = {https://www.osti.gov/biblio/22162865}, journal = {Journal of Mathematical Physics},
issn = {0022-2488},
number = 4,
volume = 54,
place = {United States},
year = {Mon Apr 15 00:00:00 EDT 2013},
month = {Mon Apr 15 00:00:00 EDT 2013}
}