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The Exponential Map for Hopf Algebras

Ghaliah Alhamzi, Edwin Beggs Orcid Logo

Symmetry, Integrability and Geometry: Methods and Applications, Volume: 18, Issue: 2022

Swansea University Author: Edwin Beggs Orcid Logo

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DOI (Published version): 10.3842/sigma.2022.017

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...

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Published in: Symmetry, Integrability and Geometry: Methods and Applications
ISSN: 1815-0659
Published: SIGMA (Symmetry, Integrability and Geometry: Methods and Application)
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URI: https://cronfa.swan.ac.uk/Record/cronfa59445
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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 1/2 densities and elements of the dual Hopf algebra. We give examples for complex valued functions on the groups S3 and Z, Woronowicz’s matrix quantum group Cq[SU2] and the Sweedler–Taft algebra.
Keywords: exponential map, Hopf algebras, geodesic
College: College of Science
Issue: 2022