Braided Hopf algebras and gauge transformations

IF 0.9 3区数学 Q3 MATHEMATICS, APPLIED

Mathematical Physics, Analysis and Geometry Pub Date : 2024-11-20 DOI:10.1007/s11040-024-09492-x

Paolo Aschieri, Giovanni Landi, Chiara Pagani

引用次数: 0

Abstract

We study infinitesimal gauge transformations of K-equivariant noncommutative principal bundles, for K a triangular Hopf algebra. They form a Lie algebra of derivations in the category of K-modules. We study Drinfeld twist deformations of these infinitesimal gauge transformations. We give several examples from abelian and Jordanian twist deformations. These include the quantum Lie algebra of gauge transformations of the instanton bundle and of the orthogonal bundle on the quantum sphere \(S^4_\theta \).

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编织霍普夫数组和规整变换

我们研究 K-三角霍普夫代数的 K-变量非交换主束的无穷小规整变换。它们构成了 K 模块范畴中的衍生列代数。我们研究这些无穷小规规变换的德林费尔德扭转变形。我们举了几个无边扭转变形和约旦扭转变形的例子。其中包括量子球\(S^4_\theta \)上的瞬子束和正交束的量子规整变换的李代数。

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

Mathematical Physics, Analysis and Geometry 数学-物理：数学物理

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： MPAG is a peer-reviewed journal organized in sections. Each section is editorially independent and provides a high forum for research articles in the respective areas. The entire editorial board commits itself to combine the requirements of an accurate and fast refereeing process. The section on Probability and Statistical Physics focuses on probabilistic models and spatial stochastic processes arising in statistical physics. Examples include: interacting particle systems, non-equilibrium statistical mechanics, integrable probability, random graphs and percolation, critical phenomena and conformal theories. Applications of probability theory and statistical physics to other areas of mathematics, such as analysis (stochastic pde''s), random geometry, combinatorial aspects are also addressed. The section on Quantum Theory publishes research papers on developments in geometry, probability and analysis that are relevant to quantum theory. Topics that are covered in this section include: classical and algebraic quantum field theories, deformation and geometric quantisation, index theory, Lie algebras and Hopf algebras, non-commutative geometry, spectral theory for quantum systems, disordered quantum systems (Anderson localization, quantum diffusion), many-body quantum physics with applications to condensed matter theory, partial differential equations emerging from quantum theory, quantum lattice systems, topological phases of matter, equilibrium and non-equilibrium quantum statistical mechanics, multiscale analysis, rigorous renormalisation group.