Affine Nijenhuis operators and Hochschild cohomology of trusses. (English) Zbl 1532.16006
This paper extends the classical Hochschild cohomology theory of rings to abelian heaps with distributing multiplication on trusses. First, the authors review some basic facts about the Hochschild cohomology. Then, they define a Nijenhuis product and examine examples and properties of Nijenhuis operators. They extend the results from linear maps to affine maps. Necessary and sufficient conditions for a Nijenhuis product on a truss are then given. Moreover, it is shown that the construction leads to compatible Lie brackets.
Reviewer: Angela Gammella-Mathieu (Metz)
MSC:
| 16E40 | (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) |
| 81R12 | Groups and algebras in quantum theory and relations with integrable systems |
Citations:
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