关于量子统计II的注记

关于量子Isometry群作用的几点注记

Some remarks on the action of Quantum Isometry Groups

本文给出了谱三元组上的一个新的充分条件，以保证定义在\cite{qorient}中的保方位保体积等距的量子群对基本的$C^*$代数具有$C^*$ -作用.

关于量子积分的注记

Remarks on Quantum Integration

我们给出了有限维辫子霍普夫代数的一般积分处方，并以N维量子超平面积分为例进行了推导。研究了积分在量子平面上的变换性质，并讨论了缺乏Hopf结构的量子群模上的积分。

关于量子仿射超代数$U_q(\hat {osp}(1,2))$的FRTS实现和Drinfeld实现的注记

A Remark On the FRTS realization and Drinfeld Realization of Quantum Affine Superalgebra $U_q(\hat {osp}(1,2))$

本文给出了量子仿射超代数$U_q(\hat {osp}(1,2))$的Faddeev-Reshetikhin-Takhtajan-Semenov-Tian-Shansky实现背后的隐藏对称性，并将q-Serre关系添加到由FRTS实现导出的$U_q(\hat {osp}(1,2))$的Drinfeld实现（math.QA/9712011）中.

关于量子对称空间构造的几点注记

Some remarks on the construction of quantum symmetric spaces

本文综述了紧致量子对称空间的构造及其用$q$ -正交多项式分析带状球函数的一些最新进展。特别地，我们在$\Uq(\gog\gol(n,\CC))$中定义了一个单参数的双边余理想族，并将相应的量子射影空间上的带状球函数表示为包含两个连续参数和一个离散参数的Askey-Wilson多项式.

Remarks on $ϕ$-coordinated modules for quantum vertex algebras

This paper is about $ϕ$-coordinated modules for weak quantum vertex algebras. Among the main results, several canonical connections among $ϕ$-coordinated modules for different $ϕ$ are established. For vertex operator algebras, a reinterpretation of Frenkel-Huang-Lepowsky's theorem on contragredient module is given in terms of $ϕ$-coordinated modules.

关于量子群作用量与核性的一点注记

A Remark on Quantum Group Actions and Nuclearity

设H是紧量子群，具有忠实Haar测度和有界计数.如果H作用在C* 代数-代数A上，我们证明了A是核的当且仅当它的不动点子代数是核的.因此H是核C* 代数.

关于量子和辫群规范理论的几点注记

Some Remarks on Quantum and Braided Group Gauge Theory

本文阐明了量子群规范理论及其最近的推广（T. Brzezinski和作者）到辫群规范理论和余代数规范理论。我们概述了编织的情况下的图解版本。我们研究的任何辫子群的玻色化提供了一个平凡的主丛在三个方面。

关于量子affine sl₂标准模块分解数的两个注记

Two remarks on decomposition numbers of standard modules for quantum affine $\mathfrak{sl}_2$

本文利用Nakajima的几何方法和最近关于特定canonical基元素的显式描述结果，推导出量子affine sl₂表示的某些分解数的闭合正公式，并获得不可约表示的q-特征标 piecewise-linear 闭合公式。

Remarks on Quantum Symmetric Algebras

We examine the quantum symmetric and exterior algebras of finite-dimensional \uqg-modules first systematically studied by Berenstein and Zwicknagl, and resolve some questions that they raised. We show that the difference (in the Grothendieck group) between the quantum symmetric and exterior cubes of a finite-dimensional module is the same as it is classically. Furthermore, we show that quantum symmetric algebras are commutative in an appropriate sense, and are universal with this property. We make extensive use of the coboundary structure on the module category.

Some remarks on the unrolled quantum group of sl(2)

In this paper we consider the representation theory of a non-standard quantization of sl(2). This paper contains several results which have applications in quantum topology, including the classification of projective indecomposable modules and a description of morphisms between them. In the process of proving these results the paper acts as a survey of the known representation theory associated to this non-standard quantization of sl(2). The results of this paper are used extensively in [arXiv:1404.7289] to study Topological Quantum Field Theory (TQFT) and have connections with Conformal Field…

A remark on quantum Hochschild homology

Beliakova-Putyra-Wehrli studied various kinds of traces, in relation to annular Khovanov homology. In particular, to a graded algebra and a graded bimodule over it, they associate a quantum Hochschild homology of the algebra with coefficients in the bimodule, and use this to obtain a deformation of the annular Khovanov homology of a link. A spectral refinement of the resulting invariant was recently given by Akhmechet-Krushkal-Willis. In this short note we observe that quantum Hochschild homology is a composition of two familiar operations, and give a short proof that it gives an invariant of …

A remark on twists and the notion of torsion-free discrete quantum groups

In this paper twists of reduced locally compact quantum groups are studied. Twists of the dual coaction on a reduced crossed product are introduced and the twisted dual coactions are proved to satisfy a type of Takesaki-Takai duality. The twisted Takesaki-Takai duality implies that twists of discrete, torsion-free quantum groups are torsion-free. Cocycle twists of duals of semisimple, compact Lie are studied leading to a locally compact quantum group contained in the Drinfeld-Jimbo algebra which gives a dual notion of Woronowicz deformations for semisimple, compact Lie groups. These cocycle tw…

Remark on Hopf images in quantum permutation groups $S_n^+$

Motivated by a question of A.~Skalski and P.M.~Sołtan about inner faithfulness of the S.~Curran's map, we revisit the results and techniques of T.~Banica and J.~Bichon's Crelle paper and study some group-theoretic properties of the quantum permutation group on $4$ points. This enables us not only to answer the aforementioned question in positive in case $n=4, k=2$, but also to classify the automorphisms of $S_4^+$, describe all the embeddings $O_{-1}(2)\subset S_4^+$ and show that all the copies of $O_{-1}(2)$ inside $S_4^+$ are conjugate. We then use these results to show that the criterion w…

关于解放量子群的 Hochschild 维数的一点注记

A remark on the Hochschild dimension of liberated quantum groups

本文研究带投影到半单代数群坐标 Hopf 代数的 Hopf 代数，利用非退化且诱导群作用非平凡的余模，证明其第三 Hochschild 同调群非平凡。

关于q-演算与可积性的注记

Remarks on q-calculus and integrability

研究了微分微积分、量子群、可积系统和q分析之间的关系。一些新的Hirota型公式建立qKP随着经典Hirota公式的变化。

关于CP ^n的约化非等价星积的注记

A Remark on Non-equivalent Star Products via Reduction for CP^n

本文利用相空间约化构造了CP^n上的非等价星积。结果表明，在相空间约化的背景下，通过将C^{n+1} {0}上U（1）作用量的动量映射变形为量子动量映射，并将相应的动量值变形为量子动量值，使得水平集i. e.量子动量映射的“约束面”与经典的一致。通过这种构造，得到了CP^n上星积的所有等价类.