3 citations · 7 across the 13 of their papers we have counts for
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Classification of contact seaweeds
Vincent E. Coll, Nicholas Russoniello
A celebrated result of Gromov ensures the existence of a contact structure on any connected, non-compact, odd dimensional Lie group. In general, such structures are not invariant u…
Contact seaweeds II: type C
Vincent E. Coll, Nicholas Russoniello
This paper is a continuation of earlier work on the construction of contact forms on seaweed algebras. In the prequel to this paper, we show that every index-one seaweed subalgebra…
On toral posets and contact Lie algebras
Nicholas W. Mayers, Nicholas Russoniello
A dimensional Lie algebra is called contact if it admits a one-form such that Here, we extend recent work to describe a combinatorial procedure…
Seaweed algebras
Alex Cameron, Vincent E. Coll, Nicholas Mayers +1
The index of a Lie algebra is an important algebraic invariant, but it is notoriously difficult to compute. However, for the suggestively-named seaweed algebras, the computation of…
The breadth of Lie poset algebras
Alex Cameron, Vincent E. Coll, Nicholas Mayers +1
The breadth of a Lie algebra is defined to be the maximal dimension of the image of , for . Here, we initiate an investigation into the breadth of th…
Contact Lie poset algebras
Vincent Coll, Nicholas Mayers, Nicholas Russoniello
We provide a combinatorial recipe for constructing all posets of height at most two for which the corresponding type-A Lie poset algebra is contact. In the case that such posets ar…
Contact Seaweeds
Vincent E. Coll, Nicholas Mayers, Nicholas Russoniello +1
A ()dimensional contact Lie algebra is one which admits a one-form such that . Such algebras have index one, but this is not generally a sufficient…
The evolution of the spectrum of a Frobenius Lie algebra under deformation
Vincent E. Coll, Nicholas Mayers, Nicholas Russoniello
The category of Frobenius Lie algebras is stable under deformation, and here we examine explicit infinitesimal deformations of four and six dimensional Frobenius Lie algebras with…
The index of nilpotent Lie poset algebras
Vincent Coll, Nicholas Mayers, Nicholas Russoniello
We establish combinatorial formulas for the index of a class of matrix Lie algebras whose matrix forms are encoded by strict partial orderings.
Classification of Frobenius, two-step solvable Lie poset algebras
Vincent Coll, Nicholas Mayers, Nicholas Russoniello
We show that the isomorphism class of a two-step solvable Lie poset subalgebra of a semisimple Lie algebra is determined by its dimension. We further establish that all such algebr…