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pro vyhledávání: '"ODESSKII IN"'
Autor:
Kontsevich, Maxim, Odesskii, Alexander
We investigate the question: for which functions $f(x_1,...,x_n),~g(x_1,...,x_n)$ the asymptotic expansion of the integral $\int g(x_1,...,x_n) e^{\frac{f(x_1,...,x_n)+x_1y_1+...+x_ny_n}{\hbar}}dx_1...dx_n$ consists only of the first term. We reveal
Externí odkaz:
http://arxiv.org/abs/2306.02178
Autor:
Kontsevich, Maxim, Odesskii, Alexander
We introduce the notion of multiplication kernels of birational and $D$-module type and give various examples. We also introduce the notion of a semi-classical multiplication kernel associated with an integrable system and discuss its quantization. F
Externí odkaz:
http://arxiv.org/abs/2105.04238
Autor:
Kontsevich, Maxim, Odesskii, Alexander
We prove that $p$-determinants of a certain class of differential operators can be lifted to power series over $\mathbb{Q}$. We compute these power series in terms of monodromy of the corresponding differential operators.
Comment: Latex, 21 page
Comment: Latex, 21 page
Externí odkaz:
http://arxiv.org/abs/2009.12159
Autor:
Odesskii, A., Sokolov, V.
We review nonabelian Poisson structures on affine and projective spaces over $\mathbb{C}$. We also construct a class of examples of nonabelian Poisson structures on $\mathbb{C} P^{n-1}$ for $n>2$. These nonabelian Poisson structures depend on a modul
Externí odkaz:
http://arxiv.org/abs/1911.03320
Autor:
Odesskii, Alexander
We construct a family of Poisson structures of hydrodynamic type on the loop space of $\mathbb{C} P^{n-1}$. This family is parametrized by the moduli space of elliptic curves or, in other words, by the modular parameter $\tau$. This family can be lif
Externí odkaz:
http://arxiv.org/abs/1901.07082
Autor:
Feigin, Boris, Odesskii, Alexander
We study flat deformations of quotients of a polynomial algebra in a class of graded commutative associative algebras. Functional equations and their solutions in terms of theta functions play important role in these studies. An analog of this theory
Externí odkaz:
http://arxiv.org/abs/1709.00750
Autor:
Odesskii, Alexander
We study representations of a free associative algebra $T^*(W\otimes W^*)$ in a vector space $V$ with the property $V\otimes V\cong V\oplus V_0$ where $T^*(W\otimes W^*)$ acts by zero on $V_0$ and the tensor product $V\otimes V$ of representations co
Externí odkaz:
http://arxiv.org/abs/1707.09384
Akademický článek
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Autor:
Odesskii, Alexander
We develop the theory of Whitham type hierarchies integrable by hydrodynamic reductions as a theory of certain differential-geometric objects. As an application we construct Gibbons-Tsarev systems associated to moduli space of algebraic curves of arb
Externí odkaz:
http://arxiv.org/abs/1609.08969
Autor:
Babela, M., Odesskii, A.
We construct a family of integrable equations of the form $v_t=f(v,v_x,v_{xx},v_{xxx})$ such that $f$ is a transcendental function in $v,v_x,v_{xx}$. This family is related to the Krichever-Novikov equation by a differential substitution. Our constru
Externí odkaz:
http://arxiv.org/abs/1608.03262