Frobenius–Schur indicators for twisted Real representation theory and two dimensional unoriented topological field theory

IF 1.6 3区数学 Q1 MATHEMATICS Journal of Geometry and Physics Pub Date : 2024-06-28 DOI:10.1016/j.geomphys.2024.105260

Levi Gagnon-Ririe, Matthew B. Young

引用次数: 0

Abstract

We construct a two dimensional unoriented open/closed topological field theory from a finite graded group $π : \hat{G} ↠ {1, - 1}$ , a π-twisted 2-cocycle $\hat{θ}$ on $B \hat{G}$ and a character $λ : \hat{G} \to U (1)$ . The underlying oriented theory is a twisted Dijkgraaf–Witten theory. The construction is based on a detailed study of the $(\hat{G}, \hat{θ}, λ)$ -twisted Real representation theory of $\ker π$ . In particular, twisted Real representations are boundary conditions of the unoriented theory and the generalized Frobenius–Schur element is its crosscap state.

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扭曲实表示论和二维无定向拓扑场论的弗罗贝尼斯-舒尔指标

我们从一个有限级数群、一个扭曲的 2-Cocycle on 和一个特征出发，构建了一个二维无定向开/闭拓扑场论。基础定向理论是一个扭曲的 Dijkgraaf-Witten 理论。这个构造基于对...的-扭曲实表示理论的详细研究。特别是，扭曲实表示是无定向理论的边界条件，广义弗罗贝纽斯-舒尔元素是它的交叉帽状态。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Geometry and Physics 物理-物理：数学物理

CiteScore

2.90

自引率

6.70%

发文量

205

审稿时长

64 days

期刊介绍： The Journal of Geometry and Physics is an International Journal in Mathematical Physics. The Journal stimulates the interaction between geometry and physics by publishing primary research, feature and review articles which are of common interest to practitioners in both fields. The Journal of Geometry and Physics now also accepts Letters, allowing for rapid dissemination of outstanding results in the field of geometry and physics. Letters should not exceed a maximum of five printed journal pages (or contain a maximum of 5000 words) and should contain novel, cutting edge results that are of broad interest to the mathematical physics community. Only Letters which are expected to make a significant addition to the literature in the field will be considered. The Journal covers the following areas of research: Methods of: • Algebraic and Differential Topology • Algebraic Geometry • Real and Complex Differential Geometry • Riemannian Manifolds • Symplectic Geometry • Global Analysis, Analysis on Manifolds • Geometric Theory of Differential Equations • Geometric Control Theory • Lie Groups and Lie Algebras • Supermanifolds and Supergroups • Discrete Geometry • Spinors and Twistors Applications to: • Strings and Superstrings • Noncommutative Topology and Geometry • Quantum Groups • Geometric Methods in Statistics and Probability • Geometry Approaches to Thermodynamics • Classical and Quantum Dynamical Systems • Classical and Quantum Integrable Systems • Classical and Quantum Mechanics • Classical and Quantum Field Theory • General Relativity • Quantum Information • Quantum Gravity

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