Related papers: Open quantum subgroups of locally compact quantum …
The structure of covariant instruments is studied and a general structure theorem is derived. A detailed characterization is given to covariant instruments in the case of an irreducible representation of a locally compact group.
A natural scheme is established for the approximation of quantum Levy processes on locally compact quantum groups by quantum random walks. We work in the somewhat broader context of discrete approximations of completely positive quantum…
The notion of normal quantum subgroup introduced in algebraic context by Parshall and Wang when applied to compact quantum groups is shown to be equivalent to the notion of normal quantum subgroup introduced by the author. As applications,…
We prove that some well known compact quantum spaces like quantum tori and some quantum two-spheres do not admit a compact quantum group structure. This is achieved by considering existence of traces, characters and nuclearity of the…
The notion of compact quantum subgroup is revisited and an alternative definition is given. Induced representations are considered and a Frobenius reciprocity theorem is obtained. A relationship between ergodic actions of compact quantum…
Landstad-Vaes theory deals with the structure of the crossed product of a C$^*$-algebra by an action of locally compact (quantum) group. In particular it describes the position of original algebra inside crossed product. The problem was…
The elements of the wide class of quantum universal enveloping algebras are prooved to be Hopf algebras $H$ with spectrum $Q(H)$ in the category of groups. Such quantum algebras are quantum groups for simply connected solvable Lie groups…
We announce various results concerning the structure of compactly generated simple locally compact groups. We introduce a local invariant, called the structure lattice, which consists of commensurability classes of compact subgroups with…
We establish a one to one correspondence between idempotent states on a locally compact quantum group G and integrable coideals in the von Neumann algebra of bounded measurable functions on G that are preserved by the scaling group. In…
Quantum computing is usually associated with discrete quantum states and physical quantities possessing discrete eigenvalue spectrum. However, quantum computing in general is any computation accomplished by the exploitation of quantum…
We describe the admissible coadjoint orbits of a compact connected Lie group and their spin-c quantization.
We introduce the analog of Bohr compactification for discrete quantum groups on C*-algebra level. The cases of unimodular and general C*-algebraic discrete quantum groups are treated separately. The passage from the former case to the…
We start with the observation that the quantum group SL_q(2), described in terms of its algebra of functions has a quantum subgroup, which is just a usual Cartan group. Based on this observation we develop a general method of constructing…
In this paper, we quantize universal gauge groups such as SU(\infty), in the sigma-C*-algebra setting. More precisely, we propose a concise definition of sigma-C*-quantum groups and explain the concept here. At the same time, we put this…
Let $G$ be an algebraic real reductive group and $Z$ a real spherical $G$-variety, that is, it admits an open orbit for a minimal parabolic subgroup $P$. We prove a local structure theorem for $Z$. In the simplest case where $Z$ is…
Idempotent states on locally compact quantum semigroups with weak cancellation properties are shown to be Haar states on a certain sub-object described by an operator system with comultiplication. We also give a characterization of the…
We classify the compact quantum groups acting on 4 points. These are the quantum subgroups of the quantum permutation group $\mathcal Q_4$. Our main tool is a new presentation for the algebra $\rm C(\mathcal Q_4)$, corresponding to an…
The structure of uniformly continuous quantum Markov semigroups with atomic decoherence-free subalgebra is established providing a naturaldecomposition of a Markovian open quantum system into its noiseless (decoherence-free) and irreducible…
We give a complete list of the one-dimensional groups definable in algebraically closed valued fields and i the pseudo-local fields, up to a finite index subgroup and a quotient by a finite subgroup.
The notion of families of quantum invertible maps ($C^*$-algebra homomorphisms satisfying Podle\'s condition) is employed to strengthen and reinterpret several results concerning universal quantum groups acting on finite quantum spaces. In…