3 citations · 5 across the 6 of their papers we have counts for
7 papers
A Pure Taxicab Perspective on Isometries
Jonathan D. Dunbar, Nathaniel Woltman
In this paper, we explicitly show the various isometries of the plane under the taxicab metric. We then use these isometries to prove that Euclid's proposition I.5 for isoscelese t…
Minimal nonnilpotent Leibniz algebras
Lindsey Bosko-Dunbar, Jonathan Dunbar, J. T. Hird +1
We classify all nonnilpotent, solvable Leibniz algebras with the property that all proper subalgebras are nilpotent. This generalizes the work of Stitzinger and Towers in Lie algeb…
Second-Maximal Subalgebras of Leibniz Algebras
Lindsey Bosko-Dunbar, Jonathan Dunbar, J. T. Hird +1
In this work we study Leibniz algebras whose second-maximal subalgebras are ideals. We provide a classification based on solvability, nilpotency, and the size of the derived algebr…
Solvable Leibniz Algebras with Abelian Nilradicals
Lindsey Bosko-Dunbar, Matthew Burke, Jonathan D. Dunbar +2
We extend the classification of solvable Lie algebras with abelian nilradicals to classify solvable Leibniz algebras which are one dimensional extensions of an abelian nilradicals.
Solvable Leibniz algebras with triangular nilradical
Lindsey Bosko-Dunbar, Matthew Burke, Jonathan Dunbar +2
A classification exists for Lie algebras whose nilradical is the triangular Lie algebra . We extend this result to a classification of all solvable Leibniz algebras with nilr…
Realization of \hat{sl}_2(C) at the Critical Level
Jonathan Dunbar, Naihuan Jing, Kailash C. Misra
An explicit realization of the affine Lie algebra \hat{sl}_2(C) at the critical level is constructed using a mixture of bosons and parafermions. Subsequently a representation of th…
Solvable Leibniz Algebras with Heisenberg Nilradical
Lindsey Bosko-Dunbar, Jonathan D. Dunbar, J. T. Hird +1
All solvable Lie algebras with Heisenberg nilradical have already been classified. We extend this result to a classification of solvable Leibniz algebras with Heisenberg nilradical…