相关论文: On Quantum Groups Co-Representations
The main notions of the quantum groups: coproduct, action and coaction, representation and corepresentation are discussed using simplest examples: $GL_q(2)$, $sl_q(2)$, $q$-oscillator algebra ${\cal A}(q)$, and reflection equation algebra.…
We study emerging notions of quantum correlations in compound systems. Based on different definitions of quantumness in individual subsystems, we investigate how they extend to the joint description of a composite system. Especially, we…
Coherent states are introduced and their properties are discussed for all simple quantum compact groups. The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general…
A new representation of Quantum Gravity is developed. This formulation is based on an extension of the group of loops. The enlarged group, that we call the Extended Loop Group, behaves locally as an infinite dimensional Lie group. Quantum…
The physical interpretation of the main notions of the quantum group theory (coproduct, representations and corepresentations, action and coaction) is discussed using the simplest examples of $q$-deformed objects (quantum group…
We present a unified approach to representations of quantum mechanics on noncommutative spaces with general constant commutators of phase-space variables. We find two phases and duality relations among them in arbitrary dimensions.…
The algebraic formulation of the quantum group gauge models in the framework of the $R$-matrix approach to the theory of quantum groups is given. We consider gauge groups taking values in the quantum groups and noncommutative gauge fields…
We introduce an explicit construction for realizing of the space of invariant deformation quantizations on an arbitrary symmetric bounded domain.
This paper is a survey on invariants of representations of quivers and their generalizations. We present the description of generating systems for invariants and relations between generators.
Quantum groups emerged in the latter quarter of the 20th century as, on the one hand, a deep and natural generalisation of symmetry groups for certain integrable systems, and on the other as part of a generalisation of geometry itself…
We introduce new representations to formulate quantum mechanics on noncommutative coordinate space, which explicitly display entanglement properties between degrees of freedom of different coordinate components and hence could be called…
Quantum groups lead to an algebraic structure that can be realized on quantum spaces. These are noncommutative spaces that inherit a well defined mathematical structure from the quantum group symmetry. In turn such quantum spaces can be…
We give an algorithm for computing matrix corepresentations for special linear and special unitary quantum groups using a combinatorial re-indexing of basis elements.
We review the application of the loop representation to gauge theories and general relativity. The emphasis lies on exhibiting the loop calculus techniques, and their application to the canonical quantization. We discuss the role that knot…
We provide formulas for invariants defined on a tensor product of defining representations of unitary groups, under the action of the product group. This situation has a physical interpretation, as it is related to the quantum mechanical…
The quantum entanglements are studied in terms of the invariants under local unitary transformations. A generalized formula of concurrence for $N$-dimensional quantum systems is presented. This generalized concurrence has potential…
This paper considers a generalization of the notion of quantum observables in ontological models of quantum mechanics. Within this framework it is possible to construct physical models where quantum noncommutativity can arise dynamically.…
We examine the notion of symmetry in quantum field theory from a fundamental representation theoretic point of view. This leads us to a generalization expressed in terms of quantum groups and braided categories. It also unifies the…
We introduce and study several amenability properties for unitary corepresentations and *-representations of algebraic quantum groups, which may be used to characterize amenability or co-amenability of such groups. As a background for this…
Quantum groups and non-commutative spaces have been repeatedly utilized in approaches to quantum gravity. They provide a mathematically elegant cut-off, often interpreted as related to the Planck-scale quantum uncertainty in position. We…