Finite-dimensional Hopf superalgebras and graded pentagon equation

IF 1.6 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2024-07-04 DOI:10.1016/j.geomphys.2024.105271

Han Dai

引用次数: 0

Abstract

Suppose that H is an arbitrary finite-dimensional Hopf superalgebra. Let $H (H)$ be the Heisenberg double of H and let $R$ be the canonical matrix of $H (H)$ that satisfies the graded pentagon equation $R_{12} R_{13} R_{23} = R_{23} R_{12}$ . It is established that H is isomorphic to the Hopf superalgebra $P (H (H), R)$ of left coefficients of $R$ . This result can be regarded as a generalisation of Militaru's result [10] from the non-super situation to the super situation.

查看原文本刊更多论文

有限维霍普夫超代数和分级五边形方程

假设 H 是任意有限维霍普夫超代数。设 H(H) 是 H 的海森堡复数，设 R 是 H(H) 的典型矩阵，满足分级五边形方程 R12R13R23=R23R12。这一结果可视为米利塔鲁结果[10]从非超情况到超情况的推广。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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