相关论文: Commuting families in skew fields and quantization…

We provide a Hodge theoretical characterization of the set of algebraic numbers which arises from the complete list, due to A. Beauville, of semistable families of elliptic curves over $\mathbb{P}^1$ with four singular fibers. Our technical…

We use compactifications of C*-algebras to introduce noncommutative coarse geometry. We transfer a noncommutative coarse structure on a C*-algebra with an action of a locally compact Abelian group by translations to Rieffel deformations and…

In a recent series of papers we have analyzed a certain deformation of the canonical commutation relations producing an interesting functional structure which has been proved to have some connections with physics, and in particular with…

Quantum spaces with $\frak{su}(2)$ noncommutativity can be modelled by using a family of $SO(3)$-equivariant differential $^*$-representations. The quantization maps are determined from the combination of the Wigner theorem for $SU(2)$ with…

Let $A:=\mathbb{C}[z_+,z_-]\otimes \Lambda(\theta_1,\theta_2,\theta_3)$, with $z_\pm$ even and $\theta_1,\theta_2,\theta_3$ odd. For a reductive Lie algebra $\mathfrak g$, let $\mathfrak g[A]:=\mathfrak g\otimes A$ be the corresponding…

In this paper, we prove a theorem that gives a simple criterion for generating commuting pairs of generalized almost complex structures on spaces that are the product of two generalized almost contact metric spaces. We examine the…

Operator nucleon vertices are constructed in composite superconformal string model. Splitting of baryon Regge trajectories with the same quantum numbers but with opposite parity is provided by inclusion of simple additional components to…

This paper develops new aspects of the interplay between shifted symplectic geometry and classical Poisson geometry, focusing on lagrangian morphisms into 2-shifted symplectic groups. We establish a Lie-type correspondence between such…

In quantum information theory and statistical physics, symmetries of multiple copies, or replicas, of a system play a pivotal role. For unitary ensembles, these symmetries are encoded in the replicated commutant: the algebra of operators…

We introduce a method to construct explicitly multiplicative 2-cocycles for bosonizations of Nichols algebras B(V) over Hopf algebras H. These cocycles arise as liftings of H-invariant linear functionals on V tensor V and give a close…

A higher dimensional analogue of the KP hierarchy is presented. Fundamental constituents of the theory are pseudo-differential operators with Moyal algebraic coefficients. The new hierarchy can be interpreted as large-$N$ limit of…

For the 3-component dispersionless Boussinesq-type system, we construct two compatible nontrivial finite deformations for the Lie algebra structure in the symmetry algebra.

To a tree of semi-simple algebras we associate a qurve (or formally smooth algebra) S. We introduce a Zariski- and etale quiver describing the finite dimensional representations of S. In particular, we show that all quotient varieties of…

We consider a class of complex manifolds constructed as multiplicative quiver varieties associated with a cyclic quiver extended by an arbitrary number of arrows starting at a new vertex. Such varieties admit a Poisson structure, which is…

The observed replication of fermions in three families is undoubtedly a reflection of a deeper symmetry underlying the standard model. In this paper we investigate one very elementary possibility, that physics above the grand unification…

In this paper, we construct new families of flag-transitive linear spaces with $q^{2n}$ points and $q^{2}$ points on each line that admit a one-dimensional affine automorphism group. We achieve this by building a natural connection with…

We construct shift operators on equivariant symplectic cohomology which generalise the shift operators on equivariant quantum cohomology in algebraic geometry. That is, given a Hamiltonian action of the torus $T$, we assign to a cocharacter…

We establish a theorem concerning the commuting scheme in characteristic p. As a significant application of this theorem, we derive an explicit lower bound for the characteristic p, ensuring the validity of the higher-dimensional Chevalley…

We are interested in Poisson structures transverse to nilpotent adjoint orbits in a complex semi-simple Lie algebra, and we study their polynomial nature, introduced by R.Cushman and M.Roberts. Furthermore, in the case of sl(n), we…

We give a constructive proof of the Hodge conjecture for complex $K3$ surfaces that does not rely on Torelli-type results. Starting with an arbitrary rational $(1,1)$-class $\alpha\in H^{1,1}(X,\mathbb{Q})$, we algorithmically build a…