scholarly journals LEFT-INVARIANT PARA-SASAKIAN STRUCTURES ON LIE GROUPS

2019 ◽  
pp. 27-37
Author(s):  
N. K. Smolentsev ◽  
Keyword(s):  
Lie Groups ◽  
Sasakian Structures

Almost contact Hom-Lie algebras and Sasakian Hom-Lie algebras

2020 ◽  
pp. 2250005
Author(s):  
E. Peyghan ◽  
L. Nourmohammadifar
Keyword(s):  
Lie Groups ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Symmetric Matrix ◽  
Contact Structures ◽  
Sasakian Structure ◽  
Sasakian Structures ◽  
Matrix Formula ◽  
Skew Symmetric Matrix

In this paper, we consider Hom-Lie groups and introduce left invariant almost contact structures on them (almost contact Hom-Lie algebras). On such Hom-Lie groups, we construct the almost contact metrics and the contact forms. We give the notion of normal almost contact Hom-Lie algebras and describe [Formula: see text]-contact and Sasakian structures on Hom-Lie algebras. Also, we study some of their properties. In addition, it is shown that any Sasakian Hom-Lie algebra is a [Formula: see text]-contact Hom-Lie algebra. Finally, we present examples of Sasakian Hom-Lie algebras and in particular, we show that the skew symmetric matrix [Formula: see text] carries a Sasakian structure.

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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