2025/09/09 by Dessislava H. Kochloukova, Kochloukova, Dessislava H., Victor Petrogradsky +1
Mathematics · #16S15 #16Z10 #17A61 #17B01 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2509.07739
openalex publication_date 2025/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Gröbner-Shirshov basis theory for Lie superalgebras by establishing a normal form theorem in terms of admissible bracketings.