Related papers: Quantum duality maps, skein algebras and their ens…
We describe a correspondence (or duality) between the q-characters of finite-dimensional representations of a quantum affine algebra and its Langlands dual in the spirit of q-alg/9708006 and 0809.4453. We prove this duality for the…
This paper contains the details and complete proofs of our earlier announcement in math.AG/9907004 . We construct a general semiregularity map for algebraic cycles as asked for by S. Bloch in 1972. The existence of such a semiregularity map…
We propose a construction of a double quasi-Poisson bracket on the group algebra associated to the twisted fundamental group of a marked oriented surface $(S,P)$ with boundary, where $P$ is a finite set of marked points on the boundary of…
In the paper, we show some properties of (reduced) stated $\mathrm{SL}(n)$-skein algebras related to their centers for essentially bordered pb surfaces, especially their centers, finitely generation over their centers, and their PI-degrees.…
We derive upper bounds for Hilbert-Schmidt's quantum coherence of general states of a $d$-level quantum system, a qudit, in terms of its incoherent uncertainty, with the latter quantified using the linear and von Neumann's entropies of the…
Let X be a cubic surface over a local number field k. Given an Azumaya algebra on X, we describe the local evaluation map X(k) -> Q/Z in two cases, showing a sharp dependence on the geometry of the reduction of X. We show that a suitably…
To each tagged triangulation of a surface with marked points and non-empty boundary we associate a quiver with potential, in such a way that whenever we apply a flip to a tagged triangulation, the Jacobian algebra of the QP associated to…
We study the birational geometry of the Kummer surfaces associated to the Jacobian varieties of genus two curves, with a particular focus on fields of characteristic two. In order to do so, we explicitly compute a projective embedding of…
We discuss how to use the recent progress in understanding of the $x$-$y$ duality and symplectic duality in the theory of topological recursion and its generalizations in order to efficiently compute the quantum spectral curve operators for…
An improved mapping of one-dimensional SU(2) non-Abelian gauge theory onto qubit degrees of freedom is presented. This new mapping allows for a reduced unphysical Hilbert space. Insensitivity to interactions within this unphysical space is…
The stated skein algebra is a generalization of the Kauffman bracket skein algebra introduced in the study of quantum trace maps. When the quantum parameter is a root of unity, the stated skein algebra has a big center and is finitely…
We introduce a framework on dual complexes for studying Arnold-type invariants of immersed curves and immersed surfaces via local finite-difference structures associated with Alexander numberings. For generic immersed plane curves and…
In this paper semirings with an idempotent addition are considered. These algebraic structures are endowed with a partial order. This allows to consider residuated maps to solve systems of inequalities $A \otimes X \preceq B$. The purpose…
This paper is devoted to study of differential calculi over quadratic algebras, which arise in the theory of quantum bounded symmetric domains. We prove that in the quantum case dimensions of the homogeneous components of the graded vector…
The Cuntz algebra carries in a natural way the structure of a module algebra over the quantized universal enveloping algebra $U_q(g)$, and the structure of a co-module algebra over the quantum group $G_q$ associated with $U_q(g)$. These two…
To each triangulation of any surface with marked points on the boundary and orbifold points of order three, we associate a quiver (with loops) with potential whose Jacobian algebra is finite dimensional and gentle. We study the stability…
We study the reciprocal complement $\mathcal{R}(D)$ of a two-dimensional finitely generated $K$-algebra $D$ by linking it with the properties of a surface with coordinate ring $D$. We give several sufficient criteria to have…
In this paper, we apply Kauffman bracket skein algebras to develop a theory of skein adequate links in thickened surfaces. We show that any alternating link diagram on a surface is skein adequate. We apply our theory to establish the first…
Quantum duality is a far reaching concept in contemporary theoretical physics. In the present paper, we reveal the quantum dualities in quantum anomalous Hall (QAH) phases through concrete two bands Hamiltonian models. Our models can…
In the present paper, we introduce two-dimensional categorified Hall algebras of smooth curves and smooth surfaces. A categorified Hall algebra is an associative monoidal structure on the stable $\infty$-category…