nilpotent subalgebras
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2020 ◽  
Vol 28 (2) ◽  
pp. 103-121
Author(s):  
David A. Towers

AbstractA finite-dimensional Lie algebra is called an A-algebra if all of its nilpotent subalgebras are abelian. These arise in the study of constant Yang-Mills potentials and have also been particularly important in relation to the problem of describing residually finite varieties. They have been studied by several authors, including Bakhturin, Dallmer, Drensky, Sheina, Premet, Semenov, Towers and Varea. In this paper we establish generalisations of many of these results to Leibniz algebras.


2017 ◽  
Vol 2019 (11) ◽  
pp. 3376-3458 ◽  
Author(s):  
Alexander Varchenko ◽  
Charles Young

Abstract We identify a class of affine hyperplane arrangements that we call cyclotomic discriminantal arrangements. We establish correspondences between the flag and Aomoto complexes of such arrangements and chain complexes for nilpotent subalgebras of Kac–Moody type Lie algebras with diagram automorphisms. As part of this construction, we find that flag complexes naturally give rise to a certain cocycle on the fixed-point subalgebras of such diagram automorphisms. As a byproduct, we show that the Bethe vectors of cyclotomic Gaudin models associated to diagram automorphisms are nonzero. We also obtain the Poincare polynomial for the cyclotomic discriminantal arrangements.


2009 ◽  
Vol 347 (9-10) ◽  
pp. 477-482 ◽  
Author(s):  
Paul Levy ◽  
George McNinch ◽  
Donna M. Testerman

2006 ◽  
Vol 34 (2) ◽  
pp. 595-600 ◽  
Author(s):  
Alexander A. Lashkhi ◽  
Irene Zimmermann

2004 ◽  
Vol 47 (3) ◽  
pp. 343-353 ◽  
Author(s):  
Vesselin Drensky ◽  
Lakhdar Hammoudi

AbstractWe construct new examples of non-nil algebras with any number of generators, which are direct sums of two locally nilpotent subalgebras. Like all previously known examples, our examples are contracted semigroup algebras and the underlying semigroups are unions of locally nilpotent subsemigroups. In our constructions we make more transparent than in the past the close relationship between the considered problem and combinatorics of words.


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