Related papers: Parameters in categorified quantum groups

Mapping-class groups of 3-manifolds feature as symmetry groups in canonical quantum gravity. They are an obvious source through which topological information could be transmitted into the quantum theory. If treated as gauge symmetries,…

Let $X$ be a differentiable manifold endowed with a transitive action $\alpha:A\times X\longrightarrow X$ of a Lie group $A$. Let $K$ be a Lie group. Under suitable technical assumptions, we give explicit classification theorems, in terms…

We formulate a notion of the quantum automorphism group of a $2$-graph. After some preliminary computations, we define quantum isomorphism between a pair of $2$-graphs. We produce a `non-trivial' example of a pair of $2$-graphs that are not…

The physical interpretation of the main notions of the quantum group theory (coproduct, representations and corepresentations, action and coaction) is discussed using the simplest examples of $q$-deformed objects (quantum group…

We revisit the results on admissible transformations between normal linear systems of second-order ordinary differential equations with an arbitrary number of dependent variables under several appropriate gauges of the arbitrary elements…

We compute the quantum isometry groups of Cuntz--Krieger algebras endowed with the spectral triples coming from the Ahlfors regular structure of the underlying topological Markov chain. This allows us to exhibit a new family of compact…

We establish equivalences of derived categories of the following 3 categories: (1) Principal block of representations of the quantum at a root of 1; (2) G-equivariant coherent sheaves on the Springer resolution; (3) Perverse sheaves on the…

We introduce some equivalent notions of homomorphisms between quantum groups that behave well with respect to duality of quantum groups. Our equivalent definitions are based on bicharacters, coactions, and universal quantum groups,…

Motivated by the vast literature of quantum automorphism groups of graphs, we define and study quantum automorphism groups of matroids. A key feature of quantum groups is that there are many quantizations of a classical group, and this…

In this article, we defined a knotted subgroup of a Lie group and considered a geometric notion of equivalence among them. We characterized these knotted subgroups in terms of one-parameter subgroups and provided examples in the case of…

To any complex Hadamard matrix we associate a quantum permutation group. The correspondence is not one-to-one, but the quantum group encapsulates a number of subtle properties of the matrix. We investigate various aspects of the…

We provide a parameterization of all fusion subcategories of the equivariantization by a group action on a fusion category. As applications, we classify the Hopf subalgebras of a family of semisimple Hopf algebras of Kac-Paljutkin type and…

One particular approach to quantum groups (matrix pseudo groups) provides the Manin quantum plane. Assuming an appropriate set of non-commuting variables spanning linearly a representation space one is able to show that the endomorphisms on…

We present the RLL-realization of extended orthosymplectic quantum supergroups for any parity sequence, with R-matrices evaluated in the earlier work arxiv:2408.16720. Our isomorphism is compatible with the internal structure of generalized…

We first compute the denominator formulas for quantum affine algebras of all exceptional types. Then we prove the isomorphisms among Grothendieck rings of categories $C_Q^{(t)}$ $(t=1,2,3)$, $\mathscr{C}_{\mathscr{Q}}^{(1)}$ and…

Let A be a finitely generated connected graded k-algebra defined by a finite number of monomial relations. Then there is a finite directed graph, Q, the Ufnarovskii graph of A, for which the categories QGr(A) and QGr(kQ) are equivalent:…

Usually the generators of a quantum group are assumed to be commutative with the noncommuting coordinates of a quantum plane. We have relaxed the assumption and investigated its consequences. Not only does a two-parameter quantum group…

In this paper we study loops, neardomains and nearfields from a categorical point of view. By choosing the right kind of morphisms, we can show that the category of neardomains is equivalent to the category of sharply 2-transitive groups.…

This paper develops a concept of 2-categorical algebraic quantum field theories (2AQFTs) that assign locally presentable linear categories to spacetimes. It is proven that ordinary AQFTs embed as a coreflective full 2-subcategory into the…

The problem of characterizing GKLS-generators and CP-maps with an invariant appeared in different guises in the literature. We prove two unifying results which hold even for weakly closed *-algebras: First, we show how to construct a normal…