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In mathematics, a pseudogroup is a set of diffeomorphisms between open sets of a space, satisfying group-like and sheaf-like properties. It is a generalisation of the concept of a group, originating however from the geometric approach of Sophus Lie to investigate symmetries of differential equations, rather than out of abstract algebra (such as quasigroup, for example). The modern theory of pseudogroups was developed by Élie Cartan in the early 1900s.

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rdfs:label	Pseudogroup (en) Псевдогруппа преобразований (ru) Псевдогрупа перетворень (uk)
rdfs:comment	In mathematics, a pseudogroup is a set of diffeomorphisms between open sets of a space, satisfying group-like and sheaf-like properties. It is a generalisation of the concept of a group, originating however from the geometric approach of Sophus Lie to investigate symmetries of differential equations, rather than out of abstract algebra (such as quasigroup, for example). The modern theory of pseudogroups was developed by Élie Cartan in the early 1900s. (en) Псевдогруппа преобразований гладкого многообразия —семейство диффеоморфизмов открытых подмножеств многообразия в , замкнутое относительно композиции отображений, перехода к обратному отображению, а также сужения и склейки отображений. (ru) Псевдогрупа перетворень гладкого многовида — сімейство дифеоморфізмів відкритих підмножин многовида у , замкнуте відносно композиції відображень, переходу до оберненого відображення, а також звуження та склейки відображень. (uk)
dct:subject	Differential geometry Algebraic structures Differential topology Lie groups
Wikipage page ID	1255458 (xsd:integer)
Wikipage revision ID	1109511501 (xsd:integer)
Link from a Wikipage to another Wikipage	Deformation theory Holomorphic function Riemann surface Vector field Lie's third theorem Lie group Lie groupoid (G,X)-manifold Differential geometry Computer algebra Analytic function Analytic manifold Mathematics Neighbourhood (mathematics) Smooth structure Quasigroup Symplectic structure Lie algebra Élie Cartan Theoretical physics Symplectic manifold Algebraic structures Topological group G-structure on a manifold Jet (mathematics) Differential topology Lie groups Current algebra Euclidean space Parameter Partial differential equation Diffeomorphism Gluing axiom Riemannian manifold Group (mathematics) Inverse function Isometry Atlas (topology) Abstract algebra Jet bundle Homeomorphism Homological algebra Differentiable manifold Manifold Sophus Lie D. C. Spencer Kunihiko Kodaira Open set Shiing-Shen Chern Formal group Symplectomorphism Flat manifold Topological space Complex variable
sameAs	Pseudogroup Pseudogroup Pseudogroup Pseudogroup Pseudogroup Pseudogroup
dbp:wikiPageUsesTemplate	dbt:Springer dbt:Cite_journal dbt:Mvar dbt:Var
author	Alekseevskii, D.V. (en)
id	p/p075710 (en)
title	Pseudo-groups (en)
has abstract	In mathematics, a pseudogroup is a set of diffeomorphisms between open sets of a space, satisfying group-like and sheaf-like properties. It is a generalisation of the concept of a group, originating however from the geometric approach of Sophus Lie to investigate symmetries of differential equations, rather than out of abstract algebra (such as quasigroup, for example). The modern theory of pseudogroups was developed by Élie Cartan in the early 1900s. (en) Псевдогруппа преобразований гладкого многообразия —семейство диффеоморфизмов открытых подмножеств многообразия в , замкнутое относительно композиции отображений, перехода к обратному отображению, а также сужения и склейки отображений. (ru) Псевдогрупа перетворень гладкого многовида — сімейство дифеоморфізмів відкритих підмножин многовида у , замкнуте відносно композиції відображень, переходу до оберненого відображення, а також звуження та склейки відображень. (uk)
prov:wasDerivedFrom	wikipedia-en:Pseudogroup?oldid=1109511501&ns=0
page length (characters) of wiki page	11868 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Pseudogroup
is Link from a Wikipage to another Wikipage of	Schwarzian derivative List of differential geometry topics Paulette Libermann Peter J. Olver Inverse semigroup Lie groupoid Timeline of manifolds

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