Related papers: On Quantum Groups Co-Representations
We consider a twisted version of quantum groups corepresentations. This generalization amounts to include in the theory the case where quantum space coordinates and its endomorphism matrix entries belong to a non-commutative quadratic…
Induced representations for quantum groups are defined starting from coisotropic quantum subgroups and their main properties are proved. When the coisotropic quantum subgroup has a suitably defined section such representations can be…
A definition is given and the physical meaning of quantum transformations of a non-commutative configuration space (quantum group coactions) is discussed. It is shown that non-commutative coordinates which are transformed by quantum groups…
It is known that any covering space of a topological group has the natural structure of a topological group. This article discusses a noncommutative generalization of this fact. A noncommutative generalization of the topological group is a…
The meaning of quantum group transformation properties is discussed in some detail by comparing the (co)actions of the quantum group with those of the corresponding Lie group, both of which have the same algebraic (matrix) form of the…
A construction of the noncommutative-geometric counterparts of classical classifying spaces is presented, for general compact matrix quantum structure groups. A quantum analogue of the classical concept of the classifying map is introduced…
We consider a constructive modification of quantum-mechanical formalism. Replacement of a general unitary group by unitary representations of finite groups makes it possible to reproduce quantum formalism without loss of its empirical…
There is a unique finite group that lies inside the 2-dimensional unitary group but not in the special unitary group, and maps by the symmetric square to an irreducible subgroup of the 3-dimensional real special orthogonal group. In an…
We introduce the construction of induced corepresentations in the setting of locally compact quantum groups and prove that the resulting induced corepresentations are unitary under some mild integrability condition. We also establish a…
Quantum-mechanical concepts can be formulated in constructive finite terms without loss of their empirical content if we replace a general unitary group by a unitary representation of a finite group. Any linear representation of a finite…
We study unitarity of the induced representations from coisotropic quantum subgroups which were introduced in math.QA/9804138. We define a real structure on coisotropic subgroups which determines an involution on the homogeneous space. We…
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 present a novel, universal description of quantum entanglement using group theory and generalized characteristic functions. It leads to new reformulations of the separability problem, and the positivity of partial transpose (PPT)…
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 describe the notion of a quantum family of maps of a quantum space and that of a quantum commutant of such a family. Quantum commutants are quantum semigroups defined by a certain universal property. We give a few examples of these…
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.
The algebraic formulation of the quantum group covariant noncommutative geometry in the framework of the $R$-matrix approach to the theory of quantum groups is given. We consider structure groups taking values in the quantum groups and…
In this lecture, we survey a number of recent results and developments regarding the representation theory of infinite-dimensional quantum groups (quantum affine algebras and related algebras), as well as their connections with cluster…
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,…
Quantum families of maps between quantum spaces are defined and studied. We prove that quantum semigroup (and sometimes quantum group) structures arise naturally on such objects out of more fundamental properties. As particular cases we…