How to Find the Holonomy Algebra of a Lorentzian Manifold

GALAEV, Anton. How to Find the Holonomy Algebra of a Lorentzian Manifold. LETTERS IN MATHEMATICAL PHYSICS. DORDRECHT: SPRINGER, 2015, roč. 105, č. 2, s. 199-219. ISSN 0377-9017. Dostupné z: https://dx.doi.org/10.1007/s11005-014-0741-y.

Základní údaje

• Originální název: How to Find the Holonomy Algebra of a Lorentzian Manifold
• Autoři: GALAEV, Anton.
• Vydání: LETTERS IN MATHEMATICAL PHYSICS, DORDRECHT, SPRINGER, 2015, 0377-9017.

Další údaje

• Originální jazyk: angličtina
• Typ výsledku: Článek v odborném periodiku
• Obor: 10101 Pure mathematics
• Stát vydavatele: Nizozemské království
• Utajení: není předmětem státního či obchodního tajemství
• Impakt faktor: Impact factor: 1.517
• Doi: http://dx.doi.org/10.1007/s11005-014-0741-y
• UT WoS: 000348355500003
• Klíčová slova anglicky: Lorentzian manifold; holonomy group; holonomy algebra; de Rham-Wu decomposition

Anotace

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.