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Nilpotency degree of the nilradical of a solvable Lie algebra on two generators and uniserial modules associated to free nilpotent Lie algebras
(Academic Press Inc Elsevier Science, 2021-11-20)
Given a sequence d~ = (d1, . . . , dk) of natural numbers, we consider
the Lie subalgebra h of gl(d, F), where d = d1 + · · · + dk and F is a field of
characteristic 0, generated by two block upper triangular matrices D ...
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 ...
Lie bialgebra structures on 2-step nilpotent graph algebras
(Elsevier, 2018)
Abstract: 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 ...