Results 171 to 180 of about 208,984 (218)

The local limit theorem on nilpotent Lie groups

Probability theory and related fields, 2018
A local limit theorem is proven on connected, simply connected nilpotent Lie groups, for a class of generating measures satisfying a moment condition and a condition on the characteristic function of the abelianization.
Robert D. Hough
semanticscholar   +1 more source

Lie-Nilpotency Indices of Group Algebras

Bulletin of the London Mathematical Society, 1992
For an associative ring \(A\), define \(A^{[1]}\) to be \(A\) and \(A^{[n]}\) (\(n>1\)) to be the two-sided ideal of \(A\) that is generated by all \(n\)- fold Lie commutators \([a_ 1,[a_ 2,\dots,[a_{n-1},a_ n]\dots]]\) (\(a_ i\in A\)). \(A\) is called Lie-nilpotent if \(A^{[n]}=0\) for some \(n\), in which case the smallest such \(n\) is denoted \(t_ ...
Bhandari, Ashwani K., Passi, I. B. S.
openaire   +1 more source

Optimal Control on Nilpotent Lie Groups

Journal of Dynamical and Control Systems, 2002
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Monroy-Pérez, F., Anzaldo-Meneses, A.
openaire   +1 more source

Automorphism Groups of Nilpotent Lie Algebras

Journal of the London Mathematical Society, 1987
It is shown that every linear algebraic group (over an arbitrary field) arises from some nilpotent Lie algebra \(L\) as the group of linear transformations induced on the commutator quotient \(L/[L,L]\) by the automorphism group of \(L\). More precisely, let \(k\) be a field and let \(K\) be an extension field of \(k\).
openaire   +2 more sources

Subsemigroups of nilpotent Lie groups

2020
Summary: For a closed subsemigroup \(S\) of a simply connected nilpotent Lie group \(G\), we prove that either \(S\) is a subgroup, or there is an epimorphism \(f\) from \(G\) to the reals \(R\) such that \(f(s) \ge 0\) for all \(s\) of \(S\).
Abels, Herbert, Vinberg, Ernest B.
openaire   +2 more sources

Group algebras of torsion groups and Lie nilpotence

Journal of Group Theory, 2010
Let \(FG\) be a group algebra of a group \(G\) over a field \(F\) and * is an involution in \(FG\). Then the subset \(FG^-=\{x\in FG\mid x^*=-x\}\) is a Lie algebra. The main result of the paper (Theorem 1.1) is the following. Suppose that \(G\) is a torsion group with no elements of order 2, \(F\) is a field of characteristic \(p\neq 2\) and * is an ...
GIAMBRUNO, Antonino, Polcino Milies, C, Sehgal, Sudarshan   +2 more
openaire   +3 more sources

Residually Lie nilpotent group rings

Archiv der Mathematik, 1992
Let \(RG\) be the group ring of the group \(G\) over the associative ring \(R\). For \(n \geq 1\) define \(RG^{[1]}\) to be \(RG\) and for \(n > 1\) to be the two-sided ideal of \(RG\) generated by all left-normed Lie commutators \([x_ 1,x_ 2,\dots,x_ n]\) \((x_ i \in RG)\), where \(ab-ba=[a,b]\). The group ring \(RG\) is said to be Lie nilpotent, if \(
Bhandari, A. K., Passi, I. B. S.
openaire   +2 more sources

Lie nilpotence of group rings

Communications in Algebra, 1993
Let FG be the group algebra of a group G over a field F. Denote by ∗ the natural involution, (∑fi gi -1. Let S and K denote the set of symmetric and skew symmetric and skew symmetric elements respectively with respect to this involutin. It is proved that if the characteristic of F is zero p≠2 and G has no 2-elements, then the Lie nilpotence of S or K ...
Antonio Giambruno, Sudarshan K. Sehgal
openaire   +1 more source

Lie Nilpotent Group Algebras and Upper Lie Codimension Subgroups

Communications in Algebra, 2006
In this article we introduce the series of the upper Lie codimension subgroups of a group algebra KG of a group G over a field K. By means of this series we give a contribution to the conjecture cl L (KG) = cl L (KG) when G belongs to particular classes of finite p-groups.
CATINO, Francesco, SPINELLI, Ernesto
openaire   +2 more sources

Fourier transforms of $C^*$-algebras of nilpotent Lie groups

, 2014
For any nilpotent Lie group $G$ we provide a description of the image of its $C^*$-algebra through its operator-valued Fourier transform. Specifically, we show that $C^*(G)$ admits a finite composition series such that that the spectra of the ...
I. Beltiţă, D. Beltiţă, J. Ludwig
semanticscholar   +1 more source