A heat semigroup version of Bernstein's theorem on Lie groups

1990 ◽  
Vol 110 (2) ◽  
pp. 101-114
Author(s):  
G. I. Gaudry ◽  
S. Meda ◽  
R. Pini
Keyword(s):  
Lie Groups ◽  
Heat Semigroup ◽  
Semigroup Version

scholarly journals The subelliptic heat kernel on the three-dimensional solvable Lie groups

2015 ◽  
Vol 27 (4) ◽  
Author(s):  
Fabrice Baudoin ◽  
Matthew Cecil
Keyword(s):  
Heat Kernel ◽  
Lie Groups ◽  
Three Dimensional ◽  
Heat Kernels ◽  
Heat Semigroup ◽  
Solvable Lie Groups ◽  
New Type ◽  
Gradient Bounds

AbstractWe study the subelliptic heat kernels of the CR three-dimensional solvable Lie groups. We first classify all left-invariant sub-Riemannian structures on three-dimensional solvable Lie groups and obtain representations of these groups. We give expressions for the heat kernels on these groups and obtain heat semigroup gradient bounds using a new type of curvature-dimension inequality.

scholarly journals Weak amenability of Lie groups made discrete

2018 ◽  
Vol 297 (1) ◽  
pp. 101-116
Author(s):  
Søren Knudby
Keyword(s):  
Lie Groups ◽  
Weak Amenability

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.

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