量子代数
We complete the classification of the pointed Hopf algebras with finite Gelfand-Kirillov dimension that are liftings of the Jordan plane over a nilpotent-by-finite group, correcting the statement in arXiv:1512.09271.
We study irreducible representations of a class of quantum spheres, quotients of quantum symplectic spheres.
In this paper, we study fusion categories which contain a proper fusion subcategory with maximal rank. They can be viewed as generalizations of near-group fusion categories. We first prove that they admit spherical structure. We then…
We describe the structure of a generalized near-group fusion category and present an example of this class of fusion categories which arises from the extension of a Fibonacci category. We then classify slightly degenerate generalized…
This paper is to establish a natural connection between regular representations for a vertex operator algebra $V$ and $A_{n}(V)$-$A_{m}(V)$ bimodules of Dong and Jiang. Let $W$ be a weak $V$-module and let $(m,n)$ be a pair of nonnegative…
We give a lattice theoretical interpretation of generalized deep holes of the Leech lattice VOA $V_\Lambda$. We show that a generalized deep hole defines a "true" automorphism invariant deep hole of the Leech lattice. We also show that…
In this paper we classify all Morita equivalent pairs of (classical) generalized Weyl algebras for generic values of the parameters, thus positively settling a 30 year old question posed by T.Hodges. We also prove a similar result for…
We study the deformation complex of the dg wheeled properad of $\mathbb{Z}$-graded quadratic Poisson structures and prove that it is quasi-isomorphic to the even M. Kontsevich graph complex. As a first application we show that the…
In this paper we present solutions to the non-commutative geometrical version of the Yang-Mills-Scalar-Matter theory in the Hopf fibration using the $3D$--calculus.
We study quantization schemes on a K\"ahler manifold and relate several interesting structures. We first construct Fedosov's star products on a K\"ahler manifold $X$ as quantizations of Kapranov's $L_\infty$-algebra structure. Then we…
Ocneanu rigidity implies that there are finitely many (braided) fusion categories with a given set of fusion rules. While there is no method for determining all such categories up to equivalence, there are a few cases for which can. For…
The Turaev-Viro state sum invariant can be extended to 3-manifolds with free boundaries. We use this fact to describe generalized Frobenius-Schur indicators as Turaev-Viro invariants of solid tori. This provides a geometric understanding of…
We contribute to the classification of Hopf algebras with finite Gelfand-Kirillov dimension, GK-dimension for short, through the study of Nichols algebras over $\mathbb{D}_{\infty}$, the infinite dihedral group. We find all the irreducible…
We prove that the spaces $\operatorname{tot}\big(\Gamma(\Lambda^\bullet A^\vee \otimes_R\mathcal{T}_{\operatorname{poly}}^{\bullet}\big)$ and $\operatorname{tot}\big(\Gamma(\Lambda^\bullet…
Using the method of Elias-Hogancamp and combinatorics of toric braids we give an explicit formula for the triply graded Khovanov-Rozansky homology of an arbitrary torus knot, thereby proving some of the conjectures of Aganagic-Shakirov,…
We obtain explicit formulas for the $1$-point functions of all states in the symmetrized Heisenberg algebra $M^+$ and symmetrized lattice VOAs $V_L^+$. For this we employ a new $\mathbf Z_2$-twisted variant of so-called Zhu recursion.
In this paper we define two Lie operations, and with that we define the bicharacter algebras, Nichols bicharacter algebras, quantum Nichols bicharacter algebras, etc. We obtain explicit bases for $\mathfrak L(V)${\tiny $_{R}$} and…
We construct a canonical deformation quantization for symplectic supermanifolds. This gives a novel proof of the super-analogue of Fedosov quantization. Our proof uses the formalism of Gelfand-Kazhdan descent, whose foundations we establish…
Convergence and analytic extension are of fundamental importance in the mathematical construction and study of conformal field theory. We review some main convergence results, conjectures and problems in the construction and study of…
In this paper, we study modular categories whose Galois group actions on their simple objects are transitive. We show that such modular categories admit unique factorization into prime transitive factors. The representations of…