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arXiv · 2509.07739

HNN extensions of Lie superalgebras

Dessislava H. Kochloukova·Victor Petrogradsky
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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.

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Dessislava H. Kochloukova, Victor Petrogradsky. 2025-09-09. HNN extensions of Lie superalgebras. https://arxiv.org/abs/2509.07739

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