HNN extensions of Lie superalgebras
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909779072385024 |
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| author | Kochloukova, Dessislava H. Petrogradsky, Victor |
| author_facet | Kochloukova, Dessislava H. Petrogradsky, Victor |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_07739 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | HNN extensions of Lie superalgebras Kochloukova, Dessislava H. Petrogradsky, Victor Rings and Algebras 17B01, 17A61, 16Z10, 16S15 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. |
| title | HNN extensions of Lie superalgebras |
| topic | Rings and Algebras 17B01, 17A61, 16Z10, 16S15 |
| url | https://arxiv.org/abs/2509.07739 |