arXiv math/98110601998-11math.QA

Symmetries of a generic coaction

Teodor Banica

备注：: 12 pages, amslatex. v2 contains detailed proofs of the 3 corollaries, to appear in Math. Ann
发表信息：: Math. Ann. 314 (1999), 763-780

英文摘要：

If B is C*-algebra of finite dimension n>3 then the finite dimensional irreducible representations of the compact quantum automorphism group of B, say G, have the same fusion rules as the ones of SO(3). As consequences, we get (1) a structure result for G in the case where B is a matrix algebra (2) if n>4 then the dual of G is not amenable (3) the fixed point subfactor P^G\subset (B\otimes P)^G has index n and principal graph A_\infty.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Quantum symmetries of the deformation quantization of $SU(3)$

We prove a criterion of when a coaction of a compact Lie group on an algebra of continuous functions on a compact manifold extends to a coaction of deformation quantizations of the Lie group and the algebra. We compute an explicit example of a compact quantum group $SU(3)_θ$, which arises as a deformation quantization of the Lie group $SU(3)$ by an action of its maximal torus. Using the criterion, we determine exactly when the action of $SU(3)$ on $S^5$ extends to a coaction of $SU(3)_θ$ on the noncommutative 5-sphere $S^5_{θ'}$. Furthermore, this coaction is shown to be cotransitive. A coacti…

2018-04-03math.QA

Irreducible tensor operators in the regular coaction formalisms of compact quantum group algebras

The defining conditions for the irreducible tensor operators associated with the unitary irreducible corepresentions of compact quantum group algebras are deduced first in both the right and left regular coaction formalisms. In each case it is shown that there are {\em{two}} types of irreducible tensor operator, which may be called `ordinary' and `twisted'. The consistency of the definitions is demonstrated, and various consequences are deduced, including generalizations of the Wigner-Eckart theorem for both the ordinary and twisted operators. Also included are discussions (within the regular …

1996-06-03math.QAq-alg

Ergodic coactions with large multiplicity and monoidal equivalence of quantum groups

We construct new examples of ergodic coactions of compact quantum groups, in which the multiplicity of an irreducible corepresentation can be strictly larger than the dimension of the latter. These examples are obtained using a bijective correspondence between certain ergodic coactions on C*-algebras and unitary fiber functors on the representation category of a compact quantum group. We classify these unitary fiber functors on the universal orthogonal and unitary quantum groups. The associated C*-algebras and von Neumann algebras can be defined by generators and relations, but are not yet wel…

2005-03-14math.OAmath.QA

Physical Meaning of Quantum Space-Time Symmetries

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 are the natural generalization of the notion of a tensor operator for usual groups and that the quantum group coactions induce semigroups of transformations of states of a system. Two examples of non-commutative transformations and the corresponding semigroups are considered.

1997-01-31hep-thmath.QAq-alg

关于量子对称性的分类

On the classification of quantum symmetries

Lomonosov Moscow State University（莫斯科国立罗蒙诺索夫大学）

本文研究了量子对称性的分类问题，通过分析Hopf代数作用与对偶作用的关系，提出cosupport分类方法，并展示了有限维代数在特定条件下Hopf代数co作用的非平凡性。

2026-08-04math.GRmath.QAmath.RA

Particles and Quantum Symmetries

The concept of quantum commutativity with respect to an action or coaction of a given Hopf algebra is used for the algebraic description of a system of particles and their interaction with certain quantum field. Graded commutativity and particles in singular magnetic field are considered as a particular example of the general formalism. The corresponding statistics and generalized Pauli exclusion principle are also mentioned.

1998-05-27math-phmath.MPmath.QA

更多相关论文收起更多论文

对称monoidal范畴中的量子Hopf刚性

Quantum Hopf rigidity in symmetric monoidal categories

该研究在对称monoidal范畴中证明，保持结合代数结构与余乘法的Hopf代数余作用自动保持其余单位等结构，推广统一了量子群仅具经典对称性的相关结果。

2026-09-09math.CTmath.QAmath.RA

A note on quivers with symmetries

We show that the bases of irreducible integrable highest weight module of a non-symmetric Kac-Moody algebra, which is associated to a quiver with a nontrivial admissible automorphism, can be naturally identified with a set of certain invariant Langrangian irreducible subvarieties of certain varieties associated with the quiver defined by Nakajima. In the case of non-symmetric affine or finite Kac-Moody algebras, the bases can be naturally identified with a set of certain invariant Langrangian irreducible subvarieties of a particular deformation of singularities of the moduli space of instanton…

1997-07-02hep-thmath.QAq-alg

Resonance Gyrons and Quantum Geometry

We describe irreducible representations, coherent states and star-products for algebras of integrals of motions (symmetries) of two-dimensional resonance oscillators. We demonstrate how the quantum geometry (quantum Kähler form, metric, quantum Ricci form, quantum reproducing measure) arises in this problem. We specifically study the distinction between the isotropic resonance $1:1$ and the general $l:m$ resonance for arbitrary coprime $l,m$. Quantum gyron is a dynamical system in the resonance algebra. We derive its Hamiltonian in irreducible representations and calculate the semiclassical as…

2005-11-07math.QA

Symmetries of quantum spaces. Subgroups and quotient spaces of quantum $SU(2)$ and $SO(3)$ groups

We prove that each action of a compact matrix quantum group on a compact quantum space can be decomposed into irreducible representations of the group. We give the formula for the corresponding multiplicities in the case of the quotient quantum spaces. We describe the subgroups and the quotient spaces of quantum SU(2) and SO(3) groups.

1994-02-11hep-thmath.OAmath.QA

*随机变量在经典概率和自由概率中de Finetti类型定理的完整分类

Full classification of de Finetti type theorems for *-random variables in classical and free probability

本文研究了*随机变量在经典和自由概率中de Finetti型定理的分类，证明了这些定理仅存在有限类型，并与Banica和Speicher引入的容易量子群相关。

2025-12-18math.OAmath.PRmath.QA

谱融合变形用于局部紧量子群

Spectral Fusion Deformations for Locally Compact Quantum Groups

本文提出了一种基于谱融合数据的局部紧量子群变形框架，通过显式代数恒等式和融合3-上同调生成新的变形方法，区分了代数一致性与分析可执行性。

2026-01-17math.FAmath.KTmath.OA

有限空间的任意子量子对称性

Anyonic quantum symmetries of finite spaces

本研究构造了量子置换群的辫子类似物，证明其为特定范畴中作用于有限空间的通用辫子紧量子群，验证了循环图的辫子量子对称性并推广了Banica的结果，还描述了该类似物的不可约表示与融合规则。

2023-11-20math.OAmath.QA

Symmetry algebra for the generic superintegrable system on the sphere

The goal of the present paper is to provide a detailed study of irreducible representations of the algebra generated by the symmetries of the generic quantum superintegrable system on the $d$-sphere. Appropriately normalized, the symmetry operators preserve the space of polynomials. Under mild conditions on the free parameters, maximal abelian subalgebras of the symmetry algebra, generated by Jucys-Murphy elements, have unique common eigenfunctions consisting of families of Jacobi polynomials in $d$ variables. We describe the action of the symmetries on the basis of Jacobi polynomials in terms…

2018-01-30math-phmath.MPmath.QA

Tridiagonal Symmetries of Models of Nonequilibrium Physics

We study the boundary symmetries of models of nonequilibrium physics where the steady state behaviour strongly depends on the boundary rates. Within the matrix product state approach to many-body systems the physics is described in terms of matrices defining a noncommutative space with a quantum group symmetry. Boundary processes lead to a reduction of the bulk symmetry. We argue that the boundary operators of an interacting system with simple exclusion generate a tridiagonal algebra whose irreducible representations are expressed in terms of the Askey-Wilson polynomials. We show that the boun…

2008-07-28cond-mat.stat-mechmath-phmath.MP

Quantum Chains of Hopf Algebras with Quantum Double Cosymmetry

Given a finite dimensional C^*-Hopf algebra H and its dual H^ we construct the infinite crossed product A=... x H x H^ x H ... and study its superselection sectors in the framework of algebraic quantum field theory. A is the observable algebra of a generalized quantum spin chain with H-order and H^-disorder symmetries, where by a duality transformation the role of order and disorder may also appear interchanged. If H=\CC G is a group algebra then A becomes an ordinary G-spin model. We classify all DHR-sectors of A --- relative to some Haag dual vacuum representation --- and prove that their sy…

1997-08-05hep-lathep-thmath.QA