22 citations · 73 across the 13 of their papers we have counts for
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The tower of Kontsevich deformations for Nambu-Poisson structures on : dimension-specific micro-graph calculus
Ricardo Buring, Arthemy V. Kiselev
In Kontsevich's graph calculus, internal vertices of directed graphs are inhabited by multi-vectors, e.g., Poisson bi-vectors; the Nambu-determinant Poisson brackets are differenti…
The Kontsevich graph orientation morphism revisited
Arthemy V. Kiselev, Ricardo Buring
The orientation morphism associates differential-polynomial flows on spaces of bi-vectors on finite-dimensional affine manif…
The orientation morphism: from graph cocycles to deformations of Poisson structures
Ricardo Buring, Arthemy Kiselev
We recall the construction of the Kontsevich graph orientation morphism which maps cocycles in the non-oriented graph complex to infinitesimal symm…
The heptagon-wheel cocycle in the Kontsevich graph complex
Ricardo Buring, Arthemy Kiselev, Nina Rutten
The real vector space of non-oriented graphs is known to carry a differential graded Lie algebra structure. Cocycles in the Kontsevich graph complex, expressed using formal sums of…
Infinitesimal deformations of Poisson bi-vectors using the Kontsevich graph calculus
Ricardo Buring, Arthemy V. Kiselev, Nina Rutten
Let be a Poisson structure on a finite-dimensional affine real manifold. Can be deformed in such a way that it stays Poisson? The language of Kontsevich graphs provides a u…
The expansion mod and computer-assisted proof schemes in the Kontsevich deformation quantization
Ricardo Buring, Arthemy Kiselev
The Kontsevich deformation quantization combines Poisson dynamics, noncommutative geometry, number theory, and calculus of oriented graphs. To manage the algebra and differential c…