Related papers: Enriched Herds And Finite Quantum Groupoids

This is a presentation of recent work on quantum permutation groups, complex Hadamard matrices, and the connections between them. A long list of problems is included. We include as well some conjectural statements, about matrix models.

We survey new results on finite groups of birational transformations of algebraic varieties.

We study the behaviors of quantum groups under an edge contraction. We show that there exists an explicit embedding induced by an edge contraction operation. We further conjecture that this explicit embedding is a section of an explicit…

We develop a theory of weighted colimits in the framework of weakly bienriched $\infty$-categories, an extension of Lurie's notion of enriched $\infty$-categories. We prove an existence result for weighted colimits, study weighted colimits…

Motivated by the orthogonality relations for irreducible characters of a finite group, we evaluate the sum of a finite group of linear characters of a Hopf algebra, at all grouplike and skew-primitive elements. We then discuss results for…

In this work we give a generalization of matched pairs of (finite) groups to describe a general class of depth two inclusions of factor von Neumann algebras and the C*-quantum groupoids associated with, using double groupoids.

We study the second bounded cohomology of an amalgamated free product of groups, and an HNN extension of a group. As an application, we have a group with infinitely many ends has infinite dimensional second bounded cohomology.

A classical theorem of Frucht states that any finite group appears as the automorphism group of a finite graph. In the quantum setting the problem is to understand the structure of the compact quantum groups which can appear as quantum…

In this report we summarize this work, all finite simple groups $G$ can determined uniformly using their orders $|G|$ and the set $\pi_e(G)$ of their element orders.

By using twist construction, we obtain a quantum groupoid $\cald\ot_{q}\uqg$ for any simple Lie algebra $\frakg$. The underlying Hopf algebroid structure encodes all the information of the corresponding elliptic quantum group-the quasi-Hopf…

A quasi-schemoid is a small category with a particular partition of the set of morphisms. We define a homotopy relation on the category of quasi-schemoids and study its fundamental properties. As a homotopy invariant, the homotopy set of…

In this article, I study some classes of finitely presented groups with the aim of finding out whether the maximal metabelian quotients of the members of these classes admit finite presentations. The considered classes include those of…

In the present paper we propose a geometric model of the twisted K-theory corresponding to elements of finite order in $H^3(X, \mathbb{Z})\times [X, \BBSU_\otimes]$.

The quantization of vector bundles is defined. Examples are constructed for the well controlled case of equivariant vector bundles over compact coadjoint orbits. (Coadjoint orbits are symplectic spaces with a transitive, semisimple symmetry…

The dead-end depth of an element g of a group with finite generating set A is the distance from g to the complement of the radius d(1,g) closed ball, in the word metric d associated to A. We exhibit a finitely presented group K with two…

In this paper we define complex equivariant K-theory for actions of Lie groupoids using finite-dimensional vector bundles. For a Bredon-compatible Lie groupoid, this defines a periodic cohomology theory on the category of finite equivariant…

Let $\phi:G\rightarrow G$ be an endomorphism of a finitely generated residually finite group. R.~Hirshon asked if there exists~$n$ such that the restriction of $\phi$ to $\phi^n(G)$ is injective. We give an example to show that this is not…

It was recently proven by Esnault, Shusterman and the second named author, that the \'etale fundamental group of a connected smooth projective variety over an algebraically closed field $k$ is finitely presented. In this note, we extend…

For a non-arithmetic Veech surface, it is known that the set points having finite orbit under the Veech group, called the set of periodic points, is finite. However, few examples of these periodic point sets have been computed. In what…

We describe the infinite dihedral group as automaton group. We collect basic results and give full proofs in details for all statements.