Results 51 to 60 of about 538,257 (210)
Nilpotent Elements in Lie Algebras
Journal of Algebra, 1990 A classical result of \textit{Fine} and \textit{Herstein} is that the number of n by n nilpotent matrices with entries in GF(q) is a power of q, that power being \(n^ 2-n\). Kaplansky formulates an analogous problem in Lie algebras as follows: For a simple Lie algebra L of n by n matrices with entries from a field of q elements, is the number of ...
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The diagonal dimension of sub‐C∗$\mathrm{C}^*$‐algebras
Proceedings of the London Mathematical Society, Volume 133, Issue 4, October 2026.Abstract We introduce diagonal dimension, a version of nuclear dimension for diagonal sub-C∗$\text{sub-}\mathrm{C}^*$‐algebras (sometimes also referred to as diagonal C∗$\mathrm{C}^*$‐pairs). Our concept has good permanence properties and detects more refined information than nuclear dimension.
Kang Li +2 more
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SEMIPRIME AND NILPOTENT FUZZY LIE ALGEBRAS
Journal of New Theory, 2016 – In this paper, we have introduced the concept of semiprime fuzzy Lie algebra and proved that every fuzzy Lie algebra of semiprime (nilpotent) Lie algebra is a semiprime (nilpotent)
Nour Alhouda Alhayek, Samer Sukkary
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Journal of High Energy Physics, 2021 Starting from type IIB string theory on an ADE singularity, the (2, 0) little string arises when one takes the string coupling g s to 0. In this setup, we give a unified description of the codimension-two defects of the little string, labeled by a simple
Nathan Haouzi, Can Kozçaz
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On Derivations and Holomorphs of Nilpotent Lie Algebras [PDF]
Nagoya Mathematical Journal, 1971 A linear Lie algebra is called toroidal if it is abelian and consists of semi-simple transformations. The maximum, t(L), of the dimensions of the toroidal subalgebras of the derivation algebra, Δ(L), is an invariant of L. This paper is mainly concerned with the relation between the magnitude of t(L) for nilpotent L and the structures of L and Δ(L).
Leger, G., Luks, E.
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The probability of generating finite and profinite groups
Journal of the London Mathematical Society, Volume 114, Issue 3, September 2026.Abstract Famously, every finite simple group G$G$ can be generated by a pair of elements. Moreover, Liebeck and Shalev (1995) proved that the probability that a pair of elements generate G$G$ tends to 1 as |G|→∞$|G| \rightarrow \infty$. In this paper, we generalize this theorem of Liebeck and Shalev. Work of Lucchini and Menegazzo (1997) implies that a
Scott Harper, Martyn Quick
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Equidistribution in 2‐nilpotent Polish groups and triple restricted sumsets
Journal of the London Mathematical Society, Volume 114, Issue 3, September 2026.Abstract The aim of this paper is to establish a Ratner‐type equidistribution theorem for orbits on homogeneous spaces associated with 2$\hskip.001pt 2$‐nilpotent locally compact Polish groups under the action of a countable discrete abelian group.
Ethan Ackelsberg, Asgar Jamneshan
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The Frattini p-subalgebra of a solvable Lie p-algebra [PDF]
, 1997 In this paper we continue our study of the Frattini p-subalgebra of a Lie p-algebra L. We show first that if L is solvable then its Frattini p-subalgebra is an ideal of L. We then consider Lie p-algebras L in which L^2 is nilpotent and find necessary and
Towers, David, Lincoln, Mark
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Controllability of affine control systems on graded Lie groups
Kuwait Journal of Science, 2015 This paper is concerned with an affine control system on a manifold which is equivalentby diffeomorphism to an invariant system on a free nilpotent Lie group, if and only if,the vector fields of the system generate graded Lie algebra and the vector ...
MEMET KULE
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From Groups to Leibniz Algebras: Common Approaches, Parallel Results [PDF]
Advances in Group Theory and Applications, 2018 In this article, we study (locally) nilpotent and hyper-central Leibniz algebras. We obtained results similar to those in group theory. For instance, we proved a result analogous to the Hirsch-Plotkin Theorem for locally nilpotent groups.
L.A. Kurdachenko +2 more
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