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- Group_contraction abstract "In theoretical physics, Eugene Wigner and Erdal Inönü have discussed the possibility to obtain from a given Lie group a different (non-isomorphic) Lie groupby a group contraction with respect to a continuous subgroup of it. That amounts to a limiting operation on a parameter of the Lie algebra, altering the structure constants of thisLie algebra in a nontrivial (singular) manner, under suitable circumstances. For example, the Lie algebra of SO(3), [X1,X2] = X3, etc, may be rewritten by a change of variables Y1= εX1, Y2=εX2, Y3=X3,as [Y1,Y2] =ε2 Y3, [Y2,Y3] = Y1, [Y3,Y1] = Y2.The contraction limit ε → 0 trivializes the first commutator and thus yields the non-isomorphic algebra of the plane Euclidean group, E2 ~ ISO(2). (This is isomorphic to the cylindrical group, describing motions of a point on the surface of a cylinder. It is the little group of null 4-vectors.) Specifically, the translation generators Y1, Y2, now generate the Abelian normal subgroup of E2 (cf. Group extension), the parabolic Lorentz transformations.Similar limits, of considerable application in physics (cf. Correspondence principles), contract the de Sitter group SO(4,1) ~ Sp(2,2) to the Poincaré group ISO(3,1), as the de Sitter radius diverges, R → ∞; or the Lorentz group to the Galilei group, as c → ∞; or the Moyal bracket Lie algebra (equivalent to quantum commutators) to the Poisson bracket Lie algebra, in the classical limit, ħ→0 .".
- Group_contraction wikiPageID "34976899".
- Group_contraction wikiPageRevisionID "585990345".
- Group_contraction hasPhotoCollection Group_contraction.
- Group_contraction subject Category:Lie_algebras.
- Group_contraction subject Category:Lie_groups.
- Group_contraction type Abstraction100002137.
- Group_contraction type Algebra106012726.
- Group_contraction type Cognition100023271.
- Group_contraction type Content105809192.
- Group_contraction type Discipline105996646.
- Group_contraction type Group100031264.
- Group_contraction type KnowledgeDomain105999266.
- Group_contraction type LieAlgebras.
- Group_contraction type LieGroups.
- Group_contraction type Mathematics106000644.
- Group_contraction type PsychologicalFeature100023100.
- Group_contraction type PureMathematics106003682.
- Group_contraction type Science105999797.
- Group_contraction comment "In theoretical physics, Eugene Wigner and Erdal Inönü have discussed the possibility to obtain from a given Lie group a different (non-isomorphic) Lie groupby a group contraction with respect to a continuous subgroup of it. That amounts to a limiting operation on a parameter of the Lie algebra, altering the structure constants of thisLie algebra in a nontrivial (singular) manner, under suitable circumstances.".
- Group_contraction label "Group contraction".
- Group_contraction sameAs m.0j679m8.
- Group_contraction sameAs Q5611219.
- Group_contraction sameAs Q5611219.
- Group_contraction sameAs Group_contraction.
- Group_contraction wasDerivedFrom Group_contraction?oldid=585990345.
- Group_contraction isPrimaryTopicOf Group_contraction.