Classification of Lie Groups with the Haagerup Property

2001 ◽  
pp. 41-61
Author(s):  
Pierre-Alain Cherix ◽  
Michael Cowling ◽  
Alain Valette
Keyword(s):  
Lie Groups ◽  
Haagerup Property

Classification of Lie Groups with the Haagerup Property

2001 ◽  
pp. 41-61
Author(s):  
Pierre-Alain Cherix ◽  
Michael Cowling ◽  
Alain Valette
Keyword(s):  
Lie Groups ◽  
Haagerup Property

Classification of 3-dimensional left-invariant almost paracontact metric structures

2017 ◽  
Vol 17 (3) ◽  
Author(s):  
Giovanni Calvaruso ◽  
Antonella Perrone
Keyword(s):  
Lie Groups ◽  
Three Dimensional ◽  
Complete Classification ◽  
Natural Assumption ◽  
Geometric Properties ◽  
3 Dimensional ◽  
Metric Structures

AbstractWe study left-invariant almost paracontact metric structures on arbitrary three-dimensional Lorentzian Lie groups. We obtain a complete classification and description under a natural assumption, which includes relevant classes as normal and almost para-cosymplectic structures, and we investigate geometric properties of these structures.

scholarly journals Algebraic Families of Harish-Chandra Pairs

2018 ◽  
Vol 2020 (15) ◽  
pp. 4776-4808 ◽  
Author(s):  
Joseph Bernstein ◽  
Nigel Higson ◽  
Eyal Subag
Keyword(s):  
Lie Groups ◽  
Reductive Group ◽  
Complete Classification ◽  
Compact Form ◽  
The Family

Abstract Mathematical physicists have studied degenerations of Lie groups and their representations, which they call contractions. In this paper we study these contractions, and also other families, within the framework of algebraic families of Harish-Chandra modules. We construct a family that incorporates both a real reductive group and its compact form, separate parts of which have been studied individually as contractions. We give a complete classification of generically irreducible families of Harish-Chandra modules in the case of the family associated to $SL(2,\mathbb{R})$.

scholarly journals Classification of Symmetry Lie Algebras of the Canonical Geodesic Equations of Five-Dimensional Solvable Lie Algebras

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1354 ◽  
Author(s):  
Hassan Almusawa ◽  
Ryad Ghanam ◽  
Gerard Thompson
Keyword(s):  
Lie Groups ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Vector Fields ◽  
Solvable Lie Groups ◽  
Related System ◽  
Geodesic Equations ◽  
Solvable Lie Algebras ◽  
Symmetry Algebras

In this investigation, we present symmetry algebras of the canonical geodesic equations of the indecomposable solvable Lie groups of dimension five, confined to algebras A 5 , 7 a b c to A 18 a . For each algebra, the related system of geodesics is provided. Moreover, a basis for the associated Lie algebra of the symmetry vector fields, as well as the corresponding nonzero brackets, are constructed and categorized.

Some remarks on the classification of Poisson Lie groups

1994 ◽  
pp. 1-16 ◽  
Author(s):  
Michel Cahen ◽  
Simone Gutt ◽  
John Rawnsley
Keyword(s):  
Lie Groups ◽  
Poisson Lie Groups

scholarly journals A CLASSIFICATION OF THE STABLE TYPE OF BG∧p FOR COMPACT LIE GROUPS

Topology ◽  
1999 ◽  
Vol 38 (1) ◽  
pp. 1-21 ◽  
Author(s):  
John Martino ◽  
Stewart Priddy
Keyword(s):  
Lie Groups ◽  
Compact Lie Groups ◽  
Stable Type
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