General form of deformation of Poisson superbracket
S.E.Konstein, A.G.Smirnov, I.V.Tyutin
TL;DR
This paper classifies formal deformations of the Poisson superbracket on Grassmann-valued functions, revealing new deformations beyond the standard Moyal bracket, thus expanding the understanding of super-Poisson structures.
Contribution
It provides a complete description of deformations of the Poisson superbracket, identifying novel deformations distinct from the Moyal bracket.
Findings
Additional deformations beyond the Moyal bracket are identified.
Deformations are classified up to an equivalence transformation.
The structure of deformed superbrackets on Grassmann-valued functions is characterized.
Abstract
Continuous formal deformations of the Poisson superbracket defined on compactly supported smooth functions on R^n taking values in a Grassmann algebra are described up to an equivalence transformation. It is shown that there are additional deformations which are different from the standard Moyal bracket.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models