The Exponential Map for Hopf Algebras

IF 0.9 3区物理与天体物理 Q2 MATHEMATICS

Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2022-03-09 DOI:10.3842/SIGMA.2022.017

Ghaliah Alhamzi, E. Beggs

引用次数: 0

Abstract

. We give an analogue of the classical exponential map on Lie groups for Hopf ∗ -algebras with differential calculus. The major difference with the classical case is the interpretation of the value of the exponential map, classically an element of the Lie group. We give interpretations as states on the Hopf algebra, elements of a Hilbert C ∗ -bimodule of 12 densities and elements of the dual Hopf algebra. We give examples for complex valued functions on the groups S 3 and Z , Woronowicz’s matrix quantum group C q [ SU 2 ] and the Sweedler–Taft algebra.

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Hopf代数的指数映射

.我们用微分学给出了Hopf＊-代数的李群上的经典指数映射的一个类似。与经典情况的主要区别在于对指数映射值的解释，指数映射是李群的经典元素。我们给出了关于Hopf代数上的状态、Hilbert C＊-12密度双模的元素和对偶Hopf代数的元素的解释。我们给出了群S3和Z上的复值函数、Woronowicz矩阵量子群Cq[SU2]和Sweedler–Taft代数的例子。

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

Symmetry Integrability and Geometry-Methods and Applications 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Scope Geometrical methods in mathematical physics Lie theory and differential equations Classical and quantum integrable systems Algebraic methods in dynamical systems and chaos Exactly and quasi-exactly solvable models Lie groups and algebras, representation theory Orthogonal polynomials and special functions Integrable probability and stochastic processes Quantum algebras, quantum groups and their representations Symplectic, Poisson and noncommutative geometry Algebraic geometry and its applications Quantum field theories and string/gauge theories Statistical physics and condensed matter physics Quantum gravity and cosmology.