scholarly journals Translations in simply transitive affine actions of Heisenberg type Lie groups

2003 ◽  
Vol 359 (1-3) ◽  
pp. 101-111 ◽  
Author(s):  
Tine De Cat ◽  
Karel Dekimpe ◽  
Paul Igodt
Keyword(s):  
Lie Groups ◽  
Heisenberg Type ◽  
Transitive Affine ◽  
Affine Actions

scholarly journals On affine actions of Lie groups

1998 ◽  
Vol 227 (2) ◽  
pp. 245-262 ◽  
Author(s):  
Abdelghani Zeghib
Keyword(s):  
Lie Groups ◽  
Affine Actions

scholarly journals Derivation double Lie algebras

2016 ◽  
Vol 15 (06) ◽  
pp. 1650114
Author(s):  
Dietrich Burde
Keyword(s):  
Recent Work ◽  
Lie Groups ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Classical Formula ◽  
Simple Derivation ◽  
Affine Actions

We study classical [Formula: see text]-matrices [Formula: see text] for Lie algebras [Formula: see text] such that [Formula: see text] is also a derivation of [Formula: see text]. This yields derivation double Lie algebras [Formula: see text]. The motivation comes from recent work on post-Lie algebra structures on pairs of Lie algebras arising in the study of nil-affine actions of Lie groups. We prove that there are no nontrivial simple derivation double Lie algebras, and study related Lie algebra identities for arbitrary Lie algebras.

scholarly journals Affine actions on Lie groups and post-Lie algebra structures

2012 ◽  
Vol 437 (5) ◽  
pp. 1250-1263 ◽  
Author(s):  
Dietrich Burde ◽  
Karel Dekimpe ◽  
Kim Vercammen
Keyword(s):  
Lie Groups ◽  
Lie Algebra ◽  
Affine Actions

scholarly journals Affine actions on nilpotent Lie groups

2009 ◽  
Vol 21 (5) ◽  
Author(s):  
Dietrich Burde ◽  
Karel Dekimpe ◽  
Sandra Deschamps
Keyword(s):  
Lie Groups ◽  
Nilpotent Lie Groups ◽  
Affine Actions
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