Symmetry, Integrability and Geometry: Methods and Applications
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


SIGMA:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Symmetry, Integrability and Geometry: Methods and Applications, 2023, Volume 19, 056, 22 pp.
DOI: https://doi.org/10.3842/SIGMA.2023.056 (Mi sigma1951) 		 
Affine Nijenhuis Operators and Hochschild Cohomology of Trusses

Tomasz Brzezińskiab, James Papwortha

a Department of Mathematics, Swansea University, Fabian Way, Swansea SA1 8EN, UK
b Faculty of Mathematics, University of Białystok, K. Ciołkowskiego 1M, 15-245 Białystok, Poland
Full-text PDF (400 kB)
References:
PDF
HTML
DOI: https://doi.org/10.3842/SIGMA.2023.056
Abstract: 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 Nijenhuis product and operators on trusses is then linearised to the case of affine spaces with compatible associative multiplications or associative affgebras. It is shown that this construction leads to compatible Lie brackets on an affine space.
Keywords: Nijenhuis operator, Hochschild cohomology, truss, heap, affine space.
Funding agency Grant number
National Science Centre, Poland 2019/35/B/ST1/01115
The research of Tomasz Brzeziński is partially supported by the National Science Centre, Poland, grant no. 2019/35/B/ST1/01115.
Received: April 4, 2023; in final form July 27, 2023; Published online August 4, 2023
Document Type: Article
MSC: 20N10, 16E40, 81R12
Language: English
Citation: Tomasz Brzeziński, James Papworth, “Affine Nijenhuis Operators and Hochschild Cohomology of Trusses”, SIGMA, 19 (2023), 056, 22 pp.
Citation in format AMSBIB
\Bibitem{BrzPap23}
\by Tomasz~Brzezi{\'n}ski, James~Papworth
\paper Affine Nijenhuis Operators and Hochschild Cohomology of Trusses
\jour SIGMA
\yr 2023
\vol 19
\papernumber 056
\totalpages 22
\mathnet{http://mi.mathnet.ru/sigma1951}
\crossref{https://doi.org/10.3842/SIGMA.2023.056}
Linking options:
  • https://www.mathnet.ru/eng/sigma1951
  • https://www.mathnet.ru/eng/sigma/v19/p56
    • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Symmetry, Integrability and Geometry: Methods and Applications
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024