3 citations · 7 across the 13 of their papers we have counts for
14 papers
Shellability of Kohnert posets
Celia Kerr, Nicholas W. Mayers, Nicholas Russoniello
In this paper, we are concerned with identifying among the family of posets associated with Kohnert polynomials, those whose order complex has a certain combinatorial property. In…
Contact Lie poset algebras of types B, C, and D
Nicholas Mayers, Nicholas Russoniello
We extend a recently established combinatorial index formula applying to Lie poset algebras of types B, C, and D. Then, using the extended index formula, we determine a characteriz…
Seaweed algebras and the unimodal spectrum property
Nicholas Mayers, Nicholas Russoniello
If is a Frobenius Lie algebra, then the spectrum of is an algebraic invariant equal to the multiset of eigenvalues corresponding to a particular opera…
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…
The index and spectrum of Lie poset algebras of type B, C, and D
Vincent E. Coll, Nicholas W. Mayers
In this paper, we define posets of types B, C, and D. These posets encode the matrix forms of certain Lie algebras which lie between the algebras of upper-triangular and diagonal m…