Related papers: Compact quantum stabilizer subgroups

We construct quantized versions of generic bases in quantum cluster algebras of finite and affine types. Under the specialization of $q$ and coefficients to 1, these bases are generic bases of finite and affine cluster algebras.

We categorify one half of the small quantum sl(2) at a prime root of unity. An extension of this construction to an arbitrary simply-laced case is proposed.

We give an elementary introduction to the theory of algebraic and topological quantum groups (in the spirit of S. L. Woronowicz). In particular, we recall the basic facts from Hopf (*-) algebra theory, theory of compact (matrix) quantum…

In this paper, we define normal soft int-groups and derive their some basic properties. We also investigate some relations on {\alpha}-inclusion, soft product and normal soft int-groups. Then we define normalizer, quotient group and give…

The definition and basic properties of the Burnside ring of compact Lie groups are presented, with emphasis on the analogy with the construction of the Burnside ring of finite groups.

We present some results about quasiconvex subgroups of infinite index and their products. After that we extend the standard notion of a subgroup commensurator to an arbitrary subset of a group, and generalize some of the previously known…

We study actions of compact quantum groups on type I factors, which may be interpreted as projective representations of compact quantum groups. We generalize to this setting some of Woronowicz' results concerning Peter-Weyl theory for…

An extension of Quantum Group is described. We propose to unite the quantum groups with parameter q and with parameter modularly dual to q.

These notes are an introduction to the theory of quantum symmetries of finite and infinite sets, graphs, and locally compact spaces.

We consider an arbitrary topological group $G$ definable in a structure $\mathcal M$, such that some basis for the topology of $G$ consists of sets definable in $\mathcal M$. To each such group $G$ we associate a compact $G$-space of…

In this article, by using basic properties of fuzzy soft topology we defined fuzzy soft compactness. We also introduced some basic definitions and theorems of the concept.

Any Hilbert space with composite dimension can be factorized into a tensor product of smaller Hilbert spaces. This allows to decompose a quantum system into subsystems. We propose a simple tractable model for a constructive study of…

We study the stabilities of quantum states of macroscopic systems, against noises, against perturbations from environments, and against local measurements. We show that the stabilities are closely related to the cluster property, which…

A survey of results on quantum Poincare groups and quantum Minkowski spaces is presented.

Associated to any closed subgroup $G\subset U_N^+$ is a family of toral subgroups $T_Q\subset G$, indexed by the unitary matrices $Q\in U_N$. The family $\{T_Q|Q\in U_N\}$ is expected to encode the main properties of $G$, and there are…

We explore set-stabilizability by constrained controls, and both controllability and stabilizability can be regarded as the special case of set-stabilizability. We not only clarify how to define an equilibrium point of Schr$\ddot{o}$dinger…

We develop a structure theory of connected solvable spherical subgroups in semisimple algebraic groups. Based on this theory, we obtain an explicit classification of all such subgroups up to conjugation.

We consider compact matrix quantum groups whose $N$-dimensional fundamental representation decomposes into an $(N-1)$-dimensional and a one-dimensional subrepresentation. Even if we know that the compact matrix quantum group associated to…

We introduce the coherent algebra of a compact metric measure space by analogy with the corresponding concept for a finite graph. As an application we show that upon topologizing the collection of isomorphism classes of compact metric…

We generalize categories of spatial partitions in the sense of C\'ebron-Weber by introducing new base partitions. This allows us to construct additional examples of free orthogonal quantum groups but yields the same class of spatial…