HNN extensions of Lie superalgebras
Rings and Algebras
2025-09-10 v1
Abstract
We explicitly describe the structure of HNN extensions of Lie superalgebras. We specify their bases. Moreover, we prove that the HNN extension is a direct sum of two subalgebras: original Lie superalgebra, and the free Lie superalgebra, which free generators are explicitly described. We apply this result to study finite generation of an ideal in a finitely presented Lie superalgebra. As an important tool, we develop Gr\"obner-Shirshov basis theory for Lie superalgebras by establishing a normal form theorem in terms of admissible bracketings.
Keywords
Cite
@article{arxiv.2509.07739,
title = {HNN extensions of Lie superalgebras},
author = {Dessislava H. Kochloukova and Victor Petrogradsky},
journal= {arXiv preprint arXiv:2509.07739},
year = {2025}
}