Results 151 to 160 of about 289 (183)

Optimal Control on Nilpotent Lie Groups

Journal of Dynamical and Control Systems, 2002
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Monroy-Pérez, F., Anzaldo-Meneses, A.
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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 \(k\).
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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.
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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
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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.
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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
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UNITARY REPRESENTATIONS OF NILPOTENT LIE GROUPS

Russian Mathematical Surveys, 1962
CONTENTSIntroduction § 1. Induced representations § 2. Representations of Lie algebras and infinitesimal group rings § 3. A special nilpotent group N § 4. Nilpotent Lie groups with one-dimensional centre § 5. Description of the representations of nilpotent Lie groups § 6. Orbits and representations § 7. Representations of the group ring § 8.
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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
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Yamabe Flow On Nilpotent Lie Groups

Bulletin of the Iranian Mathematical Society, 2019
Geometric flows are evolution flows of geometric structures, constructed for metrics on manifolds. These flows are used to modify and usually to improve the properties of metrics. In this paper, the Yamabe flow (based on the scalar curvature) on Lie groups with left-invariant metrics are investigated in some particular cases -- for the higher ...
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Isometry Groups of 4-Dimensional Nilpotent Lie Groups

Journal of Mathematical Sciences, 2017
A complete description of the isometry groups of left invariant metrics on 4-dimensional simply connected nilpotent Lie groups \(N\) is given. There are only two nonabelian 4-dimensional nilpotent Lie algebras - 2-nilpotent \(n_3\oplus \mathbf R\) and 3-nilpotent \(n_4\).
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