A. Kiselev

activity

20042026

most citedPoisson brackets symmetry from the pentagon-wheel cocycle in the graph complex

11 citations · 32 across the 17 of their papers we have counts for

collaborators

18 papers

math.NT2026

New integer sequence OEIS A392714 counts Wronskians: fast evaluation via late-growing permutations

Kian C. Shah, Arthemy V. Kiselev

The alternating composition of $N = 2 p$ weighted differential operators $w_{j} (x) \cdot \partial_{x}^{p}$ of strict order $p$ on the line $R ∋ x$ is again an operator of ord…

math.RA2026

Iterate Wronskians over $R^{d}$ as $N$ -ary brackets on $R [x^{1}, \dots, x^{d}]$ : the $N$ -bonacci numbers bound the highest total degrees

Markuss G. Kenins, Arthemy V. Kiselev

For the algebra $R [x^{1}, \dots, x^{d}]$ of polynomials in $d ⩾ 1$ variables, regard the complete generalised Wronskian $W_{d}^{k}$ of differential order $k ⩾ 1$ over…

math.RA2026

Explicit class of finite-dimensional polynomial algebras with Wronskians over $R^{d}$ as $N$ -ary Lie brackets: beyond $sl (2)$

Markuss G. Ķēniņš, Arthemy V. Kiselev

Lie algebra $sl (2)$ can be realised by vector fields on $R^{1} ∋ x$ with polynomial coefficients $1$ , $- 2 x$ , $- x^{2}$ ; their Wronskian determinants yield the Lie b…

math.CO2026

The alternating compositions of weighted differential operators yield the weights' Wronskian with which constant?

Kian C. Shah, Arthemy V. Kiselev

The alternated composition of $N = 2 p$ differential operators $w_{j} (x) \partial_{x}^{p}$ of strict order $p$ on the line $R ∋ x$ is again a differential operator of strict orde…

math.CO2025

Kontsevich graphs act on Nambu-Poisson brackets, VI. Open problems

Mollie S. Jagoe Brown, Arthemy V. Kiselev

Kontsevich's graphs from deformation quantisation allow encoding multi-vectors whose coefficients are differential-polynomial in components of Poisson brackets on finite-dimensiona…

math.RA2025

Jacobi identities for Wronskian determinants over multidimension

Arthemy V. Kiselev

The generalised Wronskian of differential order $k ⩾ 1$ for $N$ functions $f_{1}$ , $\dots$ , $f_{N}$ in $d ⩾ 1$ independent variables $x^{1}$ , $\dots$ , $x^{d}$ is the determ…

math.RA2025

Wronskians as $N$ -ary brackets in finite-dimensional analogues of $s l (2)$

Arthemy V. Kiselev

The Wronskian determinants (for coefficients of higher-order differential operators on the affine real line or circle) satisfy the table of Jacobi-type quadratic identities for str…

math.CO2025

Kontsevich graphs act on Nambu--Poisson brackets, V. Implementation

Mollie S. Jagoe Brown, Arthemy V. Kiselev

In this series of papers, we established that $Q_{d = 4}^{γ_{3}} (P)$ is a coboundary in 4D (paper II arXiv:2409.12555), and we presented a series of experimental results about the (non…

math.CO2025

Kontsevich graphs act on Nambu--Poisson brackets, IV. When the invisible becomes crucial

Mollie S. Jagoe Brown, Arthemy V. Kiselev

Kontsevich's graphs allow encoding multi-vectors whose coefficients are differential-polynomial in the coefficients of a given Poisson bracket on an affine real manifold. Encoding…

math.QA2024★ 2 cited

Kontsevich graphs act on Nambu--Poisson brackets, II. The tetrahedral flow is a coboundary in 4D

Mollie S. Jagoe Brown, Floor Schipper, Arthemy V. Kiselev

Kontsevich constructed a map from suitable cocycles in the graph complex to infinitesimal deformations of Poisson bi-vector fields. Under the deformations, the bi-vector fields rem…

math.QA2024★ 2 cited

Kontsevich graphs act on Nambu-Poisson brackets, I. New identities for Jacobian determinants

Arthemy V. Kiselev, Mollie S. Jagoe Brown, Floor Schipper

Nambu-determinant brackets on $R^{d} ∋ x = (x^{1}, ..., x^{d})$ , ${f, g}_{d} (x) = ρ (x) det (\partial (f, g, a_{1}, ..., a_{d - 2}) / \partial (x^{1}, ..., x^{d}))$ , with $a_{i} \in C^{\infty} (R^{d})$ and $ρ\partial_x\…

math.QA2024★ 3 cited

Kontsevich graphs act on Nambu-Poisson brackets, III. Uniqueness aspects

Floor Schipper, Mollie S Jagoe Brown, Arthemy V Kiselev

Kontsevich constructed a map between `good' graph cocycles $γ$ and infinitesimal deformations of Poisson bivectors on affine manifolds, that is, Poisson cocycles in the second Lich…

math.SG2019★ 1 cited

Universal cocycles and the graph complex action on homogeneous Poisson brackets by diffeomorphisms

Ricardo Buring, Arthemy V. Kiselev

The graph complex acts on the spaces of Poisson bi-vectors $P$ by infinitesimal symmetries. We prove that whenever a Poisson structure is homogeneous, i.e. $P = L_{V} (P)$ w.r…

math-ph2017★ 11 cited

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 $P ˙ = Q (P)$ of Poisson brackets $P$ on all affine manifolds $M^{r}$ ; ev…

math.CO2017★ 3 cited

The expansion $⋆$ mod $o ˉ (ℏ^{4})$ 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…

math.QA2016★ 3 cited

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 $⋆ = \times + ℏ {,}_{P} + o ˉ (ℏ)$ …

math-ph2013★ 5 cited

The Jacobi identity for graded-commutative variational Schouten bracket revisited

Arthemy V. Kiselev

This short note contains an explicit proof of the Jacobi identity for variational Schouten bracket in $Z_{2}$ -graded commutative setup. For the reasoning to be rigorous, it refers to…

math.DG2004★ 2 cited

On the symmetry structure of the minimal surface equation

A. V. Kiselev, G. Manno

An infinite sequence of commuting nonpolynomial contact symmetries of the two-dimensional minimal surface equation is constructed. Local and nonlocal conservation laws for $n$ -dime…

New integer sequence OEIS A392714 counts Wronskians: fast evaluation via late-growing permutations

Iterate Wronskians over Rd as N-ary brackets on R[x1,…,xd]: the N-bonacci numbers bound the highest total degrees

Explicit class of finite-dimensional polynomial algebras with Wronskians over Rd as N-ary Lie brackets: beyond sl(2)

The alternating compositions of weighted differential operators yield the weights' Wronskian with which constant?

Kontsevich graphs act on Nambu-Poisson brackets, VI. Open problems

Jacobi identities for Wronskian determinants over multidimension

Wronskians as N-ary brackets in finite-dimensional analogues of sl(2)

Kontsevich graphs act on Nambu--Poisson brackets, V. Implementation

Kontsevich graphs act on Nambu--Poisson brackets, IV. When the invisible becomes crucial

Kontsevich graphs act on Nambu--Poisson brackets, II. The tetrahedral flow is a coboundary in 4D

Kontsevich graphs act on Nambu-Poisson brackets, I. New identities for Jacobian determinants

Kontsevich graphs act on Nambu-Poisson brackets, III. Uniqueness aspects

Universal cocycles and the graph complex action on homogeneous Poisson brackets by diffeomorphisms

Poisson brackets symmetry from the pentagon-wheel cocycle in the graph complex

The expansion ⋆ mod oˉ(ℏ4) and computer-assisted proof schemes in the Kontsevich deformation quantization

On the Kontsevich ⋆-product associativity mechanism

The Jacobi identity for graded-commutative variational Schouten bracket revisited

On the symmetry structure of the minimal surface equation

Iterate Wronskians over $R^{d}$ as $N$ -ary brackets on $R [x^{1}, \dots, x^{d}]$ : the $N$ -bonacci numbers bound the highest total degrees

Explicit class of finite-dimensional polynomial algebras with Wronskians over $R^{d}$ as $N$ -ary Lie brackets: beyond $sl (2)$

Wronskians as $N$ -ary brackets in finite-dimensional analogues of $s l (2)$

The expansion $⋆$ mod $o ˉ (ℏ^{4})$ and computer-assisted proof schemes in the Kontsevich deformation quantization

On the Kontsevich $⋆$ -product associativity mechanism