Notes on Operator Categories
英文摘要:
The bicategory of normal functors between W*-categories is monoidally equivalent to the bicategory of W*-bimodules.
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。
Shigeru Yamagami
The bicategory of normal functors between W*-categories is monoidally equivalent to the bicategory of W*-bimodules.
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
Categories of W*-bimodules are shown in an explicit and algebraic way to constitute an involutive W*-bicategory.
Local presentability and monadicity of forgetful functors for operator algebraic categories
本研究将完备算子空间范畴的局部可数可表现性结论推广到非完备情形,证明算子系统等范畴的该性质,厘清多类算子代数相关范畴间遗忘函子的伴随性与单子性,并借助Kadison对偶定理研究函数论子范畴的相关性质。
Operator Categories I. T*-categories
引入T*-范畴作为C*-范畴的三元推广,构造其连结C*-范畴,将Zettl的Gelfand-Naimark表示定理推广至T*-范畴,并探讨其与C*-范畴的对偶。
Étale categories, restriction semigroups, and their operator algebras
本文定义 étale 范畴与限制半群的算子代数及半叉积代数,解决 Kudryavtseva-Lawson 问题,并证明其推广了 étale 群胚与逆半群的 C*-代数。
Many interesting examples of operator algebras, both self-adjoint and non-self-adjoint, can be constructed from directed graphs. In this survey, we overview the construction of $C^*$-algebras from directed graphs and from two generalizations of graphs: higher rank graphs and categories of paths. We also look at free semigroupoid algebras generated from graphs and higher rank graphs, with an emphasis on the left regular free semigroupoid algebra. We give examples of specific graphs and the algebras they generate, and we discuss properties such as semisimplicity and reflexivity. Finally, we prop…
We study some aspects of the functor of parabolic induction within the context of reduced group C*-algebras and related operator algebras. We explain how Frobenius reciprocity fits naturally within the context of operator modules, and examine the prospects for an operator algebraic formulation of Bernstein's reciprocity theorem (his second adjoint theorem).
In this informal expository note, we present a universal, formulaic construction of the free product of rigid $C^*$-2-categories. This construction allows for a straightforward, purely categorical formulation of the free composition of subfactors and planar algebras considered by Bisch and Jones. As an application, we explain the results of Tarrago and Wahl on free wreath products of compact quantum groups in this categorical language.
We present a systematic development of inductive limits in the categories of ordered *-vector spaces, Archimedean order unit spaces, matrix ordered spaces, operator systems and operator C*-systems. We show that the inductive limit intertwines the operation of passing to the maximal operator system structure of an Archimedean order unit space, and that the same holds true for the minimal operator system structure if the connecting maps are complete order embeddings. We prove that the inductive limit commutes with the operation of taking the maximal tensor product with another operator system, a…
This is a set of lecture notes on the operator algebraic approach to 2-dimensional conformal field theory. Representation theoretic aspects and connections to vertex operator algebras are emphasized. No knowledge on operator algebras or quantum field theory is assumed.
This is the second half of a two-part series studying tensor categories of unitary vertex operator algebras from a unitary point of view.
This is the first part in a two-part series of papers constructing a unitary structure for the modular tensor category (MTC) associated to a unitary rational vertex operator algebra (VOA).
We construct projective limit of projective sequence in the following categories: Archimedean order unit spaces with unital positive maps and operator systems with unital completely positive maps. We prove that inductive limit and projective limit in these categories are in duality, provided that the dual objects remain in the same categories and the maps are order embeddings. We generalize a result of Choi and Effros on matrix-ordered duals of finite-dimensional operator systems to separable case.
Inclusions of Operator Algebras from Tensor Categories: beyond irreducibility
本文通过单位张量范畴中的coend型构造,推导出C*代数的忠实包含,并探讨了非不可约情况下的离散性概念及紧量子群作用的统一框架。
We prove a spatial Isomorphism between two spaces of matrix valued truncated Toeplitz operators.
In this paper, we shall give an extension of operator Bellman inequality. This result is estimated via Kantorovich constant.
扫码添加微信好友,提出您的宝贵建议 👇
💡 备注请填写:网站反馈
发表机构由 AI 从论文文本抽取,如发现错误,欢迎反馈修正建议。