Detailed Information on Publication Record
2015
How to Find the Holonomy Algebra of a Lorentzian Manifold
GALAEV, AntonBasic information
Original name
How to Find the Holonomy Algebra of a Lorentzian Manifold
Authors
Edition
LETTERS IN MATHEMATICAL PHYSICS, DORDRECHT, SPRINGER, 2015, 0377-9017
Other information
Language
English
Type of outcome
Článek v odborném periodiku
Field of Study
10101 Pure mathematics
Country of publisher
Netherlands
Confidentiality degree
není předmětem státního či obchodního tajemství
Impact factor
Impact factor: 1.517
UT WoS
000348355500003
Keywords in English
Lorentzian manifold; holonomy group; holonomy algebra; de Rham-Wu decomposition
Změněno: 18/1/2024 11:13, doc. Anton Galaev, Dr. rer. nat.
Abstract
V originále
Manifolds with exceptional holonomy play an important role in string theory, supergravity and M-theory. It is explained how one can find the holonomy algebra of an arbitrary Riemannian or Lorentzian manifold. Using the de Rham and Wu decompositions, this problem is reduced to the case of locally indecomposable manifolds. In the case of locally indecomposable Riemannian manifolds, it is known that the holonomy algebra can be found from the analysis of special geometric structures on the manifold. If the holonomy algebra of a locally indecomposable Lorentzian manifold (M, g) of dimension n is different from , then it is contained in the similitude algebra . There are four types of such holonomy algebras. Criterion to find the type of is given, and special geometric structures corresponding to each type are described. To each there is a canonically associated subalgebra . An algorithm to find is provided.