[图书][B] Classification of five-dimensional lie algebras with one-dimensional subalgebras acting as subalgebras of the Lorentz algebra
J Rozum - 2016 - search.proquest.com
2016•search.proquest.com
Motivated by AZ Petrov's classification of four-dimensional Lorentzian metrics, we provide an
algebraic classification of the isometry-isotropy pairs of four-dimensional pseudo-
Riemannian metrics admitting local slices with five-dimensional isometries contained in the
Lorentz algebra. A purely Lie algebraic approach is applied with emphasis on the use of Lie
theoretic invariants to distinguish invariant algebra-subalgebra pairs. This method yields an
algorithm for identifying isometry-isotropy pairs subject to the aforementioned constraints.
algebraic classification of the isometry-isotropy pairs of four-dimensional pseudo-
Riemannian metrics admitting local slices with five-dimensional isometries contained in the
Lorentz algebra. A purely Lie algebraic approach is applied with emphasis on the use of Lie
theoretic invariants to distinguish invariant algebra-subalgebra pairs. This method yields an
algorithm for identifying isometry-isotropy pairs subject to the aforementioned constraints.
Abstract
Motivated by AZ Petrov's classification of four-dimensional Lorentzian metrics, we provide an algebraic classification of the isometry-isotropy pairs of four-dimensional pseudo-Riemannian metrics admitting local slices with five-dimensional isometries contained in the Lorentz algebra. A purely Lie algebraic approach is applied with emphasis on the use of Lie theoretic invariants to distinguish invariant algebra-subalgebra pairs. This method yields an algorithm for identifying isometry-isotropy pairs subject to the aforementioned constraints.
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