3 citations · 11 across the 9 of their papers we have counts for
10 papers
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…
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…
Nilpotent Lie and Leibniz algebras
Chelsie Batten Ray, Alexander Combs, Nicole Gin +3
We extend results on finite dimensional nilpotent Lie algebras to Leibniz algebras and counterexamples to others are found. One generator algebras are used in these examples and ar…
Codes and shifted codes
J. T. Hird, Naihuan Jing, Ernest Stitzinger
The action of the Bernstein operators on Schur functions was given in terms of codes in [CG] and extended to the analog in Schur Q-functions in [HJS]. We define a new combinatorial…
A Frattini Theory for Leibniz Algebras
Chelsie Batten, Lindsey Bosko-Dunbar, Allison Hedges +3
A Frattini theory for non-associative algebras was developed by Towers and results for particular classes of algebras have appeared in various articles. Especially plentiful are re…
Jacobson's Refinement of Engel's Theorem for Leibniz Algebras
Lindsey Bosko, J. T. Hird, Allison McAlister +2
We develop Jacobson's refinement of Engel's Theorem for Leibniz algebras. We then note some consequences of the result.
Codes and shifted codes of partitions
J. T. Hird, Naihuan Jing, Ernest Stitzinger
In a recent paper, Carrell and Goulden found a combinatorial identity of the Bernstein operators that they then used to prove Bernstein's Theorem. We show that this identity is a s…