scholarly journals Boundedness control sets for linear systems on Lie groups

2018 ◽  
Vol 16 (1) ◽  
pp. 370-379
Author(s):  
Víctor Ayala ◽  
María Torreblanca Todco
Keyword(s):  
Linear System ◽  
Lie Groups ◽  
Lie Group ◽  
Identity Element ◽  
Algebraic Condition ◽  
Control Sets ◽  
Control Set ◽  
Decomposable Groups ◽  
Systems On Lie Groups ◽  
Connected Lie Group

AbstractLet Σ be a linear system on a connected Lie group G and assume that the reachable set 𝓐 from the identity element e ∈ G is open. In this paper, we give an algebraic condition to warrant the boundedness of the existent control set with a nonempty interior containing e. We concentrate the search for the class of decomposable groups which includes any solvable group and also every compact semisimple group.

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.

Some Results in the Connective K-Theory of Lie Groups

1988 ◽  
Vol 31 (2) ◽  
pp. 194-199
Author(s):  
L. Magalhães
Keyword(s):  
Hopf Algebra ◽  
Lie Groups ◽  
Lie Group ◽  
Algebra Structure ◽  
Hopf Algebra Structure ◽  
K Theory ◽  
Torsion Free ◽  
Connected Lie Group

AbstractIn this paper we give a description of:(1) the Hopf algebra structure of k*(G; L) when G is a compact, connected Lie group and L is a ring of type Q(P) so that H*(G; L) is torsion free;(2) the algebra structure of k*(G2; L) for L = Z2 or Z.

A minimal realization for affine control systems on connected Lie groups

2017 ◽  
Vol 14 (09) ◽  
pp. 1750126
Author(s):  
A. Kara Hansen ◽  
S. Selcuk Sutlu
Keyword(s):  
Control System ◽  
Control Systems ◽  
Lie Groups ◽  
Lie Group ◽  
Canonical Projection ◽  
Minimal Realization ◽  
Realization Problem ◽  
Affine Control Systems ◽  
Affine Control System ◽  
Connected Lie Group

In this work, we study minimal realization problem for an affine control system [Formula: see text] on a connected Lie group [Formula: see text]. We construct a minimal realization by using a canonical projection and by characterizing indistinguishable points of the system.

Bernstein's theorem for compact, connected Lie groups

1986 ◽  
Vol 99 (2) ◽  
pp. 297-305 ◽  
Author(s):  
Garth I. Gaudry ◽  
Rita Pini
Keyword(s):  
Lie Groups ◽  
Lie Group ◽  
Image Position ◽  
Complex Valued ◽  
Connected Lie Group

In what follows, G will denote a compact, connected Lie group.Definition. A complex-valued function f ε L2(G) lies in the space A(G) if it can be written in the formwhereThe A(G) norm of f is the infimum of all sums (2) with respect to all decompositions (1).

LEFT INVARIANT COMPLEX STRUCTURES ON NILPOTENT SIMPLY CONNECTED INDECOMPOSABLE 6-DIMENSIONAL REAL LIE GROUPS

2007 ◽  
Vol 17 (01) ◽  
pp. 115-139 ◽  
Author(s):  
L. MAGNIN
Keyword(s):  
Automorphism Group ◽  
Normal Form ◽  
Lie Groups ◽  
Lie Algebras ◽  
Lie Group ◽  
Normal Forms ◽  
Equivalence Classes ◽  
Complex Structures ◽  
Simply Connected ◽  
Connected Lie Group

Integrable complex structures on indecomposable 6-dimensional nilpotent real Lie algebras have been computed in a previous paper, along with normal forms for representatives of the various equivalence classes under the action of the automorphism group. Here we go to the connected simply connected Lie group G0 associated to such a Lie algebra 𝔤. For each normal form J of integrable complex structures on 𝔤, we consider the left invariant complex manifold G = (G0, J) associated to G0 and J. We explicitly compute a global holomorphic chart for G and we write down the multiplication in that chart.

Ergodic elements for actions of Lie groups

1996 ◽  
Vol 16 (4) ◽  
pp. 703-717
Author(s):  
K. Robert Gutschera
Keyword(s):  
Invariant Measure ◽  
Simple Group ◽  
Lie Groups ◽  
Lie Group ◽  
Isometry Group ◽  
Group Structure ◽  
Structure Theory ◽  
Ergodic Action ◽  
Finite Invariant Measure ◽  
Connected Lie Group

AbstractGiven a connected Lie group G acting ergodically on a space S with finite invariant measure, one can ask when G will contain single elements (or one-parameter subgroups) that still act ergodically. For a compact simple group or the isometry group of the plane, or any group projecting onto such groups, an ergodic action may have no ergodic elements, but for any other connected Lie group ergodic elements will exist. The proof uses the unitary representation theory of Lie groups and Lie group structure theory.

Self-Maps of Low Rank Lie Groups at Odd Primes

2010 ◽  
Vol 62 (2) ◽  
pp. 284-304 ◽  
Author(s):  
Jelena Grbić ◽  
Stephen Theriault
Keyword(s):  
Lie Groups ◽  
Structural Properties ◽  
Lie Group ◽  
Low Rank ◽  
Rank Condition ◽  
Homotopy Classes ◽  
Simply Connected ◽  
Connected Lie Group

AbstractLet G be a simple, compact, simply-connected Lie group localized at an odd prime p. We study the group of homotopy classes of self-maps [G, G] when the rank of G is low and in certain cases describe the set of homotopy classes ofmultiplicative self-maps H[G, G]. The low rank condition gives G certain structural properties which make calculations accessible. Several examples and applications are given.

MAXIMAL TORUS ACTIONS ON SOLVMANIFOLDS AND DOUBLE COSET SPACES

1991 ◽  
Vol 02 (01) ◽  
pp. 67-76
Author(s):  
KYUNG BAI LEE ◽  
FRANK RAYMOND
Keyword(s):  
Lie Groups ◽  
Lie Group ◽  
Maximal Torus ◽  
Double Coset ◽  
Torus Action ◽  
Torus Actions ◽  
Coset Spaces ◽  
Aspherical Manifold ◽  
Aspherical Manifolds ◽  
Connected Lie Group

Any compact, connected Lie group which acts effectively on a closed aspherical manifold is a torus Tk with k ≤ rank of [Formula: see text], the center of π1 (M). When [Formula: see text], the torus action is called a maximal torus action. The authors have previously shown that many closed aspherical manifolds admit maximal torus actions. In this paper, a smooth maximal torus action is constructed on each solvmanifold. They also construct smooth maximal torus actions on some double coset spaces of general Lie groups as applications.

scholarly journals Strictification of étale stacky Lie groups

2011 ◽  
Vol 148 (3) ◽  
pp. 807-834 ◽  
Author(s):  
Giorgio Trentinaglia ◽  
Chenchang Zhu
Keyword(s):  
Fundamental Group ◽  
Lie Groups ◽  
Lie Algebra ◽  
Lie Group ◽  
Crossed Module ◽  
Simply Connected ◽  
The Given ◽  
Connected Lie Group

AbstractWe define stacky Lie groups to be group objects in the 2-category of differentiable stacks. We show that every connected and étale stacky Lie group is equivalent to a crossed module of the form (Γ,G) where Γ is the fundamental group of the given stacky Lie group and G is the connected and simply connected Lie group integrating the Lie algebra of the stacky group. Our result is closely related to a strictification result of Baez and Lauda.

scholarly journals Twisted Weyl Groups of Compact Lie Groups and Nonabelian Cohomology

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 21
Author(s):  
Ming Liu ◽  
Xia Zhang
Keyword(s):  
Weyl Group ◽  
Lie Groups ◽  
Lie Group ◽  
Weyl Groups ◽  
Module Structure ◽  
Compact Lie Groups ◽  
Compact Torus ◽  
Nonabelian Cohomology ◽  
Connected Lie Group

Given a compact connected Lie group G with an S 1 -module structure and a maximal compact torus T of G S 1 , we define twisted Weyl group W ( G , S 1 , T ) of G associated to S 1 -module and show that two elements of T are δ -conjugate if and only if they are in one W ( G , S 1 , T ) -orbit. Based on this, we prove that the natural map W ( G , S 1 , T ) \ H 1 ( S 1 , T ) → H 1 ( S 1 , G ) is bijective, which reduces the calculation for the nonabelian cohomology H 1 ( S 1 , G ) .

Sign in / Sign up

Export Citation Format

Share Document