Affine Nijenhuis Operators and Hochschild Cohomology of Trusses
The classical Hochschild cohomology theory of rings is extended to abelian heaps with distributing multiplication or trusses. This cohomology is then employed to give necessary and sufficient conditions for a Nijenhuis product on a truss (defined by the extension of the Nijenhuis product on an assoc...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2023 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2023
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211973 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Affine Nijenhuis Operators and Hochschild Cohomology of Trusses. Tomasz Brzeziński and James Papworth. SIGMA 19 (2023), 056, 22 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862594472974483456 |
|---|---|
| author | Brzeziński, Tomasz Papworth, James |
| author_facet | Brzeziński, Tomasz Papworth, James |
| citation_txt | Affine Nijenhuis Operators and Hochschild Cohomology of Trusses. Tomasz Brzeziński and James Papworth. SIGMA 19 (2023), 056, 22 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The classical Hochschild cohomology theory of rings is extended to abelian heaps with distributing multiplication or trusses. This cohomology is then employed to give necessary and sufficient conditions for a Nijenhuis product on a truss (defined by the extension of the Nijenhuis product on an associative ring introduced by Cariñena, Grabowski, and Marmo in [Internat. J. Modern Phys. A 15 (2000), 4797-4810, arXiv:math-ph/0610011]) to be associative. The definition of the Nijenhuis product and operators on trusses is then linearised to the case of affine spaces with compatible associative multiplications or associative algebras. It is shown that this construction leads to compatible Lie brackets on an affine space.
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| first_indexed | 2026-03-13T22:33:06Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211973 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-13T22:33:06Z |
| publishDate | 2023 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Brzeziński, Tomasz Papworth, James 2026-01-20T16:12:15Z 2023 Affine Nijenhuis Operators and Hochschild Cohomology of Trusses. Tomasz Brzeziński and James Papworth. SIGMA 19 (2023), 056, 22 pages 1815-0659 2020 Mathematics Subject Classification: 20N10; 16E40; 81R12 arXiv:2303.12880 https://nasplib.isofts.kiev.ua/handle/123456789/211973 https://doi.org/10.3842/SIGMA.2023.056 The classical Hochschild cohomology theory of rings is extended to abelian heaps with distributing multiplication or trusses. This cohomology is then employed to give necessary and sufficient conditions for a Nijenhuis product on a truss (defined by the extension of the Nijenhuis product on an associative ring introduced by Cariñena, Grabowski, and Marmo in [Internat. J. Modern Phys. A 15 (2000), 4797-4810, arXiv:math-ph/0610011]) to be associative. The definition of the Nijenhuis product and operators on trusses is then linearised to the case of affine spaces with compatible associative multiplications or associative algebras. It is shown that this construction leads to compatible Lie brackets on an affine space. The research of Tomasz Brzeziński is partially supported by the National Science Centre, Poland, grant no. 2019/35/B/ST1/01115. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Affine Nijenhuis Operators and Hochschild Cohomology of Trusses Article published earlier |
| spellingShingle | Affine Nijenhuis Operators and Hochschild Cohomology of Trusses Brzeziński, Tomasz Papworth, James |
| title | Affine Nijenhuis Operators and Hochschild Cohomology of Trusses |
| title_full | Affine Nijenhuis Operators and Hochschild Cohomology of Trusses |
| title_fullStr | Affine Nijenhuis Operators and Hochschild Cohomology of Trusses |
| title_full_unstemmed | Affine Nijenhuis Operators and Hochschild Cohomology of Trusses |
| title_short | Affine Nijenhuis Operators and Hochschild Cohomology of Trusses |
| title_sort | affine nijenhuis operators and hochschild cohomology of trusses |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211973 |
| work_keys_str_mv | AT brzezinskitomasz affinenijenhuisoperatorsandhochschildcohomologyoftrusses AT papworthjames affinenijenhuisoperatorsandhochschildcohomologyoftrusses |