A result of Barnea and Isaacs states that if L is a finite dimensional nilpotent Lie algebra with exactly two distinct centralizer dimensions, then nilpotency class of L is either 2 or 3. In this ...article, we classify all such finite dimensional 3-step nilpotent Lie algebras over a finite field.
In this paper we introduce an equivalence between the category of the t-nilpotent quadratic Lie algebras with d generators and the category of some symmetric invariant bilinear forms over the ...t-nilpotent free Lie algebra with d generators. Taking into account this equivalence, t-nilpotent quadratic Lie algebras with d generators are classified (up to isometric isomorphisms, and over any field of characteristic zero), in the following cases: d=2 and t≤5, d=3 and t≤3.
The purpose of this work is to give a direct proof of the multiplicative Brunn-Minkowski inequality in nilpotent Lie groups based on Hadwiger-Ohmann's one of the classical Brunn-Minkowski inequality ...in Euclidean space.
In this paper, we give a characterization of finite-dimensional nilpotent Lie algebras of breadth 3 over finite fields of odd characteristic. This characterization parallels to the one for finite ...p-groups of breadth 3 given earlier in 5.
This paper describes the centers of the universal enveloping algebras and the invariant rings of the standard filiform Lie algebras over fields of characteristic zero and also over large enough prime ...characteristic. We determine explicit generators for the quotient fields and also a compact form for the generators for the invariants rings. We prove several combinatorial results concerning the Hilbert series of these algebras.
In this paper, we obtain the structure of all non-isomorphic finite-dimensional nilpotent Lie algebras L of class 3 with derived subalgebra of dimension 3 when
For a natural number m, a Lie algebra L over a field k is said to be of breadth type
if the co-dimension of the centralizer of every non-central element is m. In this article, we classify finite ...dimensional nilpotent Lie algebras of breadth type
over
of odd characteristic up to isomorphism. We also give a partial classification of the same over finite fields of even characteristic,
and
. We also discuss 2-step nilpotent Camina Lie algebras.
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