Results 161 to 170 of about 32,301 (195)

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

GENERALIZED LIE NILPOTENT GROUP RINGS

Mathematics of the USSR-Sbornik, 1987
Translation from Mat. Sb., Nov. Ser. 129(171), No.1, 154-158 (Russian) (1986; Zbl 0601.16011).
Bovdi, A. A., Khripta, I. I.
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

ON THE RATIONAL FORMS OF NILPOTENT LIE ALGEBRAS AND LATTICES IN NILPOTENT LIE GROUPS

2002
Let \(L\) be a real finite-dimensional nilpotent Lie algebra and \(H\) be a rational subalgebra of \(L\). \(H\) is called a rational form for \(L\) if there exists a basis of \(H\) over \(Q\) which is also a real basis for \(L\). Rational forms for the Lie algebra of a nilpotent Lie group give rise to lattices in the group.
openaire   +2 more sources

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

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.
openaire   +2 more sources

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 ...
openaire   +2 more sources

Algebraic Groups of Automorphisms of Nilpotent Groups and Lie Algebras

Journal of the London Mathematical Society, 1986
It is shown that every linear algebraic group over a field of characteristic zero arises as the group of automorphisms induced on the commutator quotient L/[L,L] of some nilpotent Lie algebra L. More precisely, let K be an algebraically closed field of characteristic zero and let k be a subfield of K.
Bryant, R. M., Groves, J. R. J.
openaire   +2 more sources

Lie *-Nilpotence of Group Rings

Communications in Algebra, 2014
Let KG be the group ring of a group G over a field K. Let * be an involution of a group G extended linearly to the group ring KG. Suppose that G is a torsion group without 2-elements and K is a field with characteristic different from 2. We prove that KG is Lie *-nilpotent if and only if KG is Lie nilpotent.
openaire   +1 more source

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 \(n_4\).
openaire   +2 more sources