The Lie Group in Infinite Dimension

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26110%2F11%3APU91460" target="_blank" >RIV/00216305:26110/11:PU91460 - isvavai.cz</a>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

The Lie Group in Infinite Dimension

Original language description

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 adjustedfor 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 Liealgebra 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.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

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Continuities

Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2011

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Abstract and Applied Analysis

ISSN

1085-3375

e-ISSN

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Volume of the periodical

2011

Issue of the periodical within the volume

1

Country of publishing house

FK - FALKLAND ISLANDS (MALVINAS)

Number of pages

35

Pages from-to

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UT code for WoS article

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EID of the result in the Scopus database

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