Related papers: Braid group action and root vectors for the $q$-On…
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…
We describe a completely algebraic axiom system for intertwining operators of vertex algebra modules, using algebraic flat connections, thus formulating the concept of a {\em tree algebra}. Using the Riemann-Hilbert correspondence, we…
GL_q(N)- and SO_q(N)-covariant deformations of the completely symmetric/antisymmetric projectors with an arbitrary number of indices are explicitly constructed as polynomials in the braid matrices. The precise relation between the…
We construct an infinite tower of covering spaces over the configuration space of $n-1$ distinct non-zero points in the complex plane. This results in an action of the braid group $\mathbb{B}_n$ on the set of $n$-adic integers…
We introduce a quantum automorphism group for hypergraphs, which turns out to generalize the quantum automorphism group of Bichon for classical graphs. Further, we show that our quantum automorphism group acts on hypergraph C*-algebras as…
To a weighted graph can be associated a bipartite graph planar algebra P. We construct and study the symmetric enveloping inclusion of P. We show that this construction is equivariant with respect to the automorphism group of P. The…
Let $A,A^*$ be the generators of the $q-$Onsager algebra. Analogues of Lusztig's $r-th$ higher order relations are proposed. In a first part, based on the properties of tridiagonal pairs of $q-$Racah type which satisfy the defining…
We prove that for any natural n>1, the abstract commensurator group of the Baumslag - Solitar group BS(1,n) is isomorphic to the group of 2 by 2 upper triangular matrices A over rational numbers with A_{11}=1. We also prove that for any…
Assume that we are given a coaction \delta of a locally compact group G on a C*-algebra A and a T-valued Borel 2-cocycle \omega on G. Motivated by the approach of Kasprzak to Rieffel's deformation we define a deformation A_\omega of A.…
Let $ \mathfrak{g} $ be an untwisted affine Kac-Moody algebra over the field $ K \, $, and let $ U_q(\mathfrak{g}) $ be the associated quantum enveloping algebra; let $ \mathfrak{U}_q(g) $ be the Lusztig's integer form of $…
In this paper, we investigate the structure of the quantum affine superalgebra associated with the orthosymplectic Lie superalgebra $\mathfrak{osp}(2m+1|2n)$ for $m\geqslant 1$. The Drinfeld-Jimbo presentation for this algebra, denoted as…
The theory of characteristic functions for row contractions is used to determine the group $Aut(B(H)^n_1)$ of all free holomorphic automorphisms of the unit ball of $B(H)^n$. We show that the noncommutative Poisson transform commutes with…
In this paper, we study boundary actions of CAT(0) spaces from a point of view of topological dynamics and $C^*$-algebras. First, we investigate the actions of right-angled Coexter groups and right-angled Artin groups with finite defining…
We compute the $ K $-theory of quantum automorphism groups of finite dimensional $ C^* $-algebras in the sense of Wang. The results show in particular that the $ C^* $-algebras of functions on the quantum permutation groups $ S_n^+ $ are…
Our first collection of results parametrize (filtered) actions of a quantum Borel $U_q(\mathfrak{b}) \subset U_q(\mathfrak{sl}_2)$ on the path algebra of an arbitrary (finite) quiver. When $q$ is a root of unity, we give necessary and…
We examine the Moore complex of the Delta-group structure related to the pure braid groups and introduced by Berrick, Cohen, Wong, and Wu. We prove that the cycle and the boundary groups are invariant under all automorphisms of the pure…
The Hopf algebra generated by the l-functionals on the quantum double C_q[G] \bowtie C_q[G] is considered, where C_q[G] is the coordinate algebra of a standard quantum group and q is not a root of unity. It is shown to be isomorphic to…
Let G be a Lie group, $T^*G$ its cotangent bundle with its natural Lie group structure obtained by performing a left trivialization of T^*G and endowing the resulting trivial bundle with the semi-direct product, using the coadjoint action…
(1) Utilizing a Braid group action on a completion of U_q(\hat{sl_{n+1}}), an algebra homomorphism from the toroidal algebra U_q(sl_{n+1,tor}) (n\ge 2) with fixed parameter to a completion of U_q(\hat{gl_{n+1}}) is obtained. (2) The…
We consider groups that act on spherically symmetric rooted trees and study the associated representation of the group on the space of locally constant functions on the boundary of the tree. We introduce and discuss the new notion of…