5 papers · 1 filter
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…
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…