Generalizations for Schouten-Nijenhuis Bracket and for Differential Analog of Special Yang-Baxter Equations
Dmitrij V. Soroka, Vyacheslav A. Soroka
TL;DR
This paper extends the Schouten-Nijenhuis bracket to superspaces and opposite Grassmann parities, and introduces several generalizations of the differential analog of the special Yang-Baxter equations.
Contribution
It provides new generalizations of the Schouten-Nijenhuis bracket and the differential analog of the Yang-Baxter equations for broader mathematical contexts.
Findings
Generalized Schouten-Nijenhuis bracket for superspaces
Extended brackets for opposite Grassmann parities
New forms of differential Yang-Baxter analogs
Abstract
The Schouten-Nijenhuis bracket is generalized for the superspace case and for the Poisson brackets of opposite Grassmann parities. Quite a number of generalizations for the differential analog of the special Yang-Baxter equations is also proposed.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology