scholarly journals 3-dimensional Bol loops as sections in non-solvable Lie groups

2005 ◽  
Vol 17 (3) ◽  
Author(s):  
Ágota Figula
Keyword(s):  
Lie Groups ◽  
Solvable Lie Groups ◽  
3 Dimensional ◽  
Bol Loops

scholarly journals Minimal surfaces in 3-dimensional solvable Lie groups II

2006 ◽  
Vol 73 (3) ◽  
pp. 365-374 ◽  
Author(s):  
Jun-Ichi Inoguchi
Keyword(s):  
Integral Representation ◽  
Lie Groups ◽  
Minimal Surfaces ◽  
Representation Formula ◽  
Gauss Map ◽  
Invariant Metric ◽  
Solvable Lie Groups ◽  
3 Dimensional ◽  
Integral Representation Formula

An integral representation formula in terms of the normal Gauss map for minimal surfaces in 3-dimensional solvable Lie groups with left invariant metric is obtained.

scholarly journals Topological Loops with Decomposable Solvable Multiplication Groups

2021 ◽  
Vol 77 (1) ◽  
Author(s):  
Ameer Al-Abayechi ◽  
Ágota Figula
Keyword(s):  
Lie Groups ◽  
Lie Group ◽  
Three Dimensional ◽  
Solvable Lie Groups ◽  
3 Dimensional ◽  
Multiplication Group ◽  
Simply Connected ◽  
Solvable Lie Group

AbstractIn this paper we deal with the class $$\mathcal {C}$$ C of decomposable solvable Lie groups having dimension six. We determine those Lie groups in $$\mathcal {C}$$ C and their subgroups which are the multiplication groups Mult(L) and the inner mapping groups Inn(L) for three-dimensional connected simply connected topological loops L. This result completes the classification of the at most 6-dimensional solvable multiplication Lie groups of the loops L. Moreover, we obtain that every at most 3-dimensional connected topological proper loop having a solvable Lie group of dimension at most six as its multiplication group is centrally nilpotent of class two.

scholarly journals Harmonic morphisms from solvable Lie groups

2009 ◽  
Vol 147 (2) ◽  
pp. 389-408 ◽  
Author(s):  
SIGMUNDUR GUDMUNDSSON ◽  
MARTIN SVENSSON
Keyword(s):  
Lie Groups ◽  
Symmetric Spaces ◽  
Global Solutions ◽  
Riemannian Symmetric Space ◽  
Continuous Family ◽  
Harmonic Morphisms ◽  
Solvable Lie Groups ◽  
3 Dimensional ◽  
Riemannian Symmetric Spaces ◽  
Simply Connected

AbstractIn this paper we introduce two new methods for constructing harmonic morphisms from solvable Lie groups. The first method yields global solutions from any simply connected nilpotent Lie group and from any Riemannian symmetric space of non-compact type and rank r ≥ 3. The second method provides us with global solutions from any Damek–Ricci space and many non-compact Riemannian symmetric spaces. We then give a continuous family of 3-dimensional solvable Lie groups not admitting any complex-valued harmonic morphisms, not even locally.

scholarly journals Some groups with T1 primitive ideal spaces

1985 ◽  
Vol 38 (1) ◽  
pp. 55-64 ◽  
Author(s):  
A. L. Carey ◽  
W. Moran
Keyword(s):  
Normal Subgroup ◽  
Lie Groups ◽  
Lie Group ◽  
Locally Compact Group ◽  
Primitive Ideal ◽  
Ideal Space ◽  
Solvable Lie Groups ◽  
Locally Compact ◽  
Simply Connected ◽  
Connected Lie Group

AbstractLet G be a second countable locally compact group possessing a normal subgroup N with G/N abelian. We prove that if G/N is discrete then G has T1 primitive ideal space if and only if the G-quasiorbits in Prim N are closed. This condition on G-quasiorbits arose in Pukanzky's work on connected and simply connected solvable Lie groups where it is equivalent to the condition of Auslander and Moore that G be type R on N (-nilradical). Using an abstract version of Pukanzky's arguments due to Green and Pedersen we establish that if G is a connected and simply connected Lie group then Prim G is T1 whenever G-quasiorbits in [G, G] are closed.

Analysis of a Distinguished Laplacian on Solvable Lie Groups

1993 ◽  
Vol 163 (1) ◽  
pp. 151-162 ◽  
Author(s):  
Saverio Giulini ◽  
Giancarlo Mauceri
Keyword(s):  
Lie Groups ◽  
Solvable Lie Groups

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.

Sign in / Sign up

Export Citation Format

Share Document