Detail publikace

The Lie Group in Infinite Dimension

TRYHUK, V. CHRASTINOVÁ, V. DLOUHÝ, O.

Originální název

The Lie Group in Infinite Dimension

Typ

článek v časopise - ostatní, Jost

Jazyk

angličtina

Originální abstrakt

A Lie group acting on finite-dimensional space is generated by its infinitesimal transformations and conversely, any Lie algebra of vector fields in finite dimension generates a Lie group (the first fundamental theorem). This classical result is adjusted for the infinite-dimensional case. We prove that the (local, C^\infty smooth) action of a Lie group on infinite-dimensional space (a manifold modelled on R^\infty) may be regarded as a limit of finite-dimensional approximations and the corresponding Lie algebra of vector fields may be characterized by certain finiteness requirements. The result is applied to the theory of generalized (or higher-order) infinitesimal symmetries of differential equations.

Klíčová slova

Lie first main theorem; local one--parameter group; local Lie group; generalized infinitesimal symmetries; diffiety

Autoři

TRYHUK, V.; CHRASTINOVÁ, V.; DLOUHÝ, O.

Rok RIV

2011

Vydáno

24. 2. 2011

Nakladatel

Hindawi Publishing Corporation

Místo

USA

ISSN

1085-3375

Periodikum

Abstract and Applied Analysis

Ročník

2011

Číslo

1

Stát

Spojené státy americké

Strany od

1

Strany do

35

Strany počet

35

BibTex

@article{BUT50550,
  author="Václav {Tryhuk} and Veronika {Chrastinová} and Oldřich {Dlouhý}",
  title="The Lie Group in Infinite Dimension",
  journal="Abstract and Applied Analysis",
  year="2011",
  volume="2011",
  number="1",
  pages="1--35",
  issn="1085-3375"
}