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Nilpotency of commutative finitely generated algebras satisfying L(x)(3) + gamma L(x)(3)=0, gamma=1, 0
(ELSEVIER, 2011-03-15)
This paper deals with two varieties of commutative non-associative algebras. One variety satisfies L(x)(3) + L(x)(3) = 0. The other variety satisfies L(x)(3) = 0. We prove that in either variety, any finitely generated ...
Locally nilpotent derivations and automorphism groups of certain Danielewski surfaces
(Academic Press Inc Elsevier Science, 2017)
We describe the set of all locally nilpotent derivations of the quotient ring K[X,Y, Z]/(f (X)Y - phi(X, Z)) constructed from the defining equation f (X)Y = phi(X, Z) of a generalized Danielewski surface in K-3 for a ...
Lie bialgebra structures on 2-step nilpotent graph algebras
(Academic Press Inc Elsevier Science, 2018-07)
We generalize a result on the Heisenberg Lie algebra that gives restrictions to possible Lie bialgebra cobrackets on 2-step nilpotent algebras with some additional properties. For the class of 2-step nilpotent Lie algebras ...
A generalized Gelfand pair attached to a 3-step nilpotent Lie group
(Birkhauser Boston Inc, 2020-08-24)
Let N be a nilpotent Lie group and K a compact subgroup of the automorphism group Aut(N) of N. It is well-known that if (K⋉ N, K) is a Gelfand pair then N is at most 2-step nilpotent Lie group. The notion of Gelfand pair ...
Nilpotent Global Centers of Linear Systems with Cubic Homogeneous NonlinearitiesCentros Globales Nilpotentes de Sistemas Lineales con No-linealidades Homogéneneas Cúbicas
(International Journal of Bifurcation and Chaos, 2020)
Nilpotent Global Centers of Linear Systems with Cubic Homogeneous NonlinearitiesCentros Globales Nilpotentes de Sistemas Lineales con No-linealidades Homogéneneas Cúbicas
(International Journal of Bifurcation and Chaos, 2020)
Locally nilpotent groups of units in tiled rings
(ACADEMIC PRESS INC ELSEVIER SCIENCE, 2010)
We consider locally nilpotent subgroups of units in basic tiled rings A, over local rings O which satisfy a weak commutativity condition. Tiled rings are generalizations of both tiled orders and incidence rings. If, in ...
Nilpotency of commutative finitely generated algebras satisfying alpha r-x(3) + beta r(x)rx2=0
(Taylor & Francis, 2015)
Killing–Yano 2-forms on 2-step nilpotent Lie groups
(Springer, 2021-06-01)
In this article we show that the only 2-step nilpotent Lie groups which carry a non-degenerate left invariant Killing–Yano 2-form are the complex Lie groups. In the case of 2-step nilpotent complex Lie groups arising from ...
Free 2-step nilpotent Lie algebras and indecomposable representations
(Taylor & Francis, 2018-07)
Given an algebraically closed field F of characteristic 0 and an F-vector space V, let L(V) = V⊕Λ2(V) denote the free 2-step nilpotent Lie algebra associated to V. In this paper, we classify all uniserial representations ...