Related papers: Euler continuants in noncommutative quasi-Poisson …

We study Poisson-flat connections with logarithmic poles along a simple normal crossings divisor on a holomorphic Poisson manifold, where flatness is required only along the symplectic foliation. After identifying the relevant logarithmic…

We investigate the geometric, algebraic and homologic structures related with Poisson structure on a smooth manifold. Introduce a noncommutative foundations of these structures for a Poisson algebra. Introduce and investigate noncommutative…

We study Poisson and operator algebras with the ''quasi-linear property'' from the Heisenberg picture point of view. This means that there exists a set of one-parameter groups yielding an explicit expression of dynamical variables…

It is shown that every $2$-shifted Poisson structure on a finitely generated semi-free commutative differential graded algebra $A$ defines a very explicit infinitesimal $2$-braiding on the homotopy $2$-category of the symmetric monoidal…

We prove that quantized multiplicative quiver varieties and quantum character varieties define sheaves of Azumaya algebras over the corresponding classical moduli spaces, and we prove that the Azumaya locus of the Kauffman bracket skein…

Let $K$ be an imaginary quadratic field, $N$ be a positive integer, $f(z)$ be a newform of level $\Gamma_1(N)$, and $A_f$ be the abelian variety associated to $f$. For each $\tau \in K$ ($\operatorname{Im} \tau >0$), we construct a certain…

We use the theory of reduced determinant functors from [24] to give a new, computationally useful, description of the relative $K_0$-groups of orders in finite dimensional separable algebras that need not be commutative. By combining this…

The space of local operators in the $Q$-cohomology of the holomorphic-topological supercharge in a four-dimensional $\mathcal{N}=2$ theory carries the structure of a Poisson vertex algebra. This note studies the Poisson vertex algebra…

These notes provide an exposition on obtaining the well-known standard results of quasiregular maps on Riemannian manifolds, given the corresponding theory in the Euclidean setting. We recall several different approaches to first-order…

The canonical structure of classical non-linear sigma models on Riemannian symmetric spaces, which constitute the most general class of classical non-linear sigma models known to be integrable, is shown to be governed by a fundamental…

This text gives some results about quantum torsors. Our starting point is an old reformulation of torsors recalled recently by Kontsevich. We propose an unification of the definitions of torsors in algebraic geometry and in Poisson…

We show that the category of representations of the Euclidean group of orientation-preserving isometries of two-dimensional Euclidean space is equivalent to the category of representations of the preprojective algebra of infinite type A. We…

Given a Lie group G whose Lie algebra is endowed with a nondegenerate invariant symmetric bilinear form, we construct a Poisson algebra of continuous functions on a certain open subspace R of the space of representations in G of the…

Poisson boundary is a measurable $\Gamma$-space canonically associated with a group $\Gamma$ and a probability measure $\mu$ on it. The collection of all measurable $\Gamma$-equivariant quotients, known as $\mu$-boundaries, of the Poisson…

We give a cohomological interpretation of both the Kac polynomial and the refined Donaldson-Thomas- invariants of quivers. This interpretation yields a proof of a conjecture of Kac from 1982 and gives a new perspective on recent work of…

The moduli space of $G$-bundles on an elliptic curve with additional flag structure admits a Poisson structure. The bivector can be defined using double loop group, loop group and sheaf cohomology constructions. We investigate the links…

The question studied here is the behavior of the Poisson bracket under C^0-perturbations. In this purpose, we introduce the notion of pseudo-representation and prove that for a normed Lie algebra, it converges to a representation. An…

The Poisson bracket invariants, introduced by Buhovsky, Entov, and Polterovich and further studied by Entov and Polterovich, serve as invariants for quadruples of closed sets in symplectic manifolds. Their nonvanishing has significant…

The multisymplectic formalism of field theories developed by many mathematicians over the last fifty years is extended in this work to deal with manifolds that have boundaries. In particular, we develop a multisymplectic framework for first…

A Poisson structure on the time-extended space R x M is shown to be appropriate for a Hamiltonian formalism in which time is no more a privileged variable and no a priori geometry is assumed on the space M of motions. Possible geometries…