Nilpotent groups and lie algebras

1968 ◽  
Vol 7 (4) ◽  
pp. 206-211 ◽  
Author(s):  
K. K. Andreev
Keyword(s):  
Lie Algebras ◽  
Nilpotent Groups

Lie algebras associated with topological nilpotent groups

1975 ◽  
Vol 8 (2) ◽  
pp. 171-180 ◽  
Author(s):  
Louis Magnin ◽  
Jacques Simon
Keyword(s):  
Lie Algebras ◽  
Nilpotent Groups

Automorphisms of Free Metabelian Nilpotent Groups and Lie Algebras

1995 ◽  
Vol 52 (1) ◽  
pp. 157-165 ◽  
Author(s):  
Athanassios I. Papistas
Keyword(s):  
Lie Algebras ◽  
Nilpotent Groups

scholarly journals Completions of certain nilpotent groups

1979 ◽  
Vol 28 (4) ◽  
pp. 461-470 ◽  
Author(s):  
Siegfried Moran ◽  
Janet Williams
Keyword(s):  
Lie Algebras ◽  
Integral Domain ◽  
First Integral ◽  
Nilpotent Groups ◽  
Integral Domains

AbstractThe completions of certain nilpotent groups with respect to some ascending sequences of integral domains are constructed. These completions are generalizations of Lazard completions for the groups under consideration and they are Lie algebras over the first integral domain in the sequence. The construction is possible in particular for finite p-groups of exponent p and class < p.

scholarly journals Nilpotent Lie Algebras and Systolic Growth of Nilmanifolds

2017 ◽  
Vol 2019 (9) ◽  
pp. 2763-2799
Author(s):  
Yves Cornulier
Keyword(s):  
Lie Algebras ◽  
Lie Group ◽  
Polynomial Growth ◽  
Volume Growth ◽  
Growth Function ◽  
Nilpotent Groups ◽  
Upper Bounds ◽  
Nilpotent Lie Algebras ◽  
Open Questions ◽  
Simply Connected

Abstract Introduced by Gromov in the nineties, the systolic growth of a Lie group gives the smallest possible covolume of a lattice with a given systole. In a simply connected nilpotent Lie group, this function has polynomial growth, but can grow faster than the volume growth. We express this systolic growth function in terms of discrete cocompact subrings of the Lie algebra, making it more practical to estimate. After providing some general upper bounds, we develop methods to provide nontrivial lower bounds. We provide the first computations of the asymptotics of the systolic growth of nilpotent groups for which this is not equivalent to the volume growth. In particular, we provide an example for which the degree of growth is not an integer; it has dimension 7. Finally, we gather some open questions.

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