22 citations · 73 across the 13 of their papers we have counts for
13 papers
Associativity certificates for Kontsevich's star-product mod : unlike
Ricardo Buring, Arthemy V. Kiselev
The formula mod of Kontsevich's star-product with harmonic propagators was known in full at since 2018 for generic Poisson bracket…
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…
Kontsevich's star-product up to order 7 for affine Poisson brackets: where are the Riemann zeta values?
Ricardo Buring, Arthemy V. Kiselev
The Kontsevich star-product admits a well-defined restriction to the class of affine -- in particular, linear -- Poisson brackets; its graph expansion consists only of Kontsevich's…
The hidden symmetry of Kontsevich's graph flows on the spaces of Nambu-determinant Poisson brackets
Ricardo Buring, Dimitri Lipper, Arthemy V. Kiselev
Kontsevich's graph flows are -- universally for all finite-dimensional affine Poisson manifolds -- infinitesimal symmetries of the spaces of Poisson brackets. We show that the prev…
Formality morphism as the mechanism of -product associativity: how it works
Ricardo Buring, Arthemy Kiselev
The formality morphism , in Kontsevich's deformation quantization is a collection of maps from tensor powers of the differ…
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…
Poisson brackets symmetry from the pentagon-wheel cocycle in the graph complex
Ricardo Buring, Arthemy V. Kiselev, Nina J. Rutten
Kontsevich designed a scheme to generate infinitesimal symmetries of Poisson brackets on all affine manifolds ; ev…
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…
The Kontsevich tetrahedral flow revisited
Anass Bouisaghouane, Ricardo Buring, Arthemy V. Kiselev
We prove that the Kontsevich tetrahedral flow , the right-hand side of which is a linear combination of two differential monomi…
On the Kontsevich -product associativity mechanism
Ricardo Buring, Arthemy V. Kiselev
The deformation quantization by Kontsevich [arXiv:q-alg/9709040] is a way to construct an associative noncommutative star-product …