The Exponential Map for Hopf Algebras
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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2022 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2022
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211528 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | The Exponential Map for Hopf Algebras. Ghaliah Alhamzi and Edwin Beggs. SIGMA 18 (2022), 017, 17 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862579782471909376 |
|---|---|
| author | Alhamzi, Ghaliah Beggs, Edwin |
| author_facet | Alhamzi, Ghaliah Beggs, Edwin |
| citation_txt | The Exponential Map for Hopf Algebras. Ghaliah Alhamzi and Edwin Beggs. SIGMA 18 (2022), 017, 17 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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 ∗-bimodule of 1/2 densities, and elements of the dual Hopf algebra. We give examples for complex-valued functions on the groups ₃ and ℤ, Woronowicz's matrix quantum group ℂq[₂], and the Sweedler-Taft algebra.
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| first_indexed | 2026-03-13T16:53:20Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211528 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-13T16:53:20Z |
| publishDate | 2022 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Alhamzi, Ghaliah Beggs, Edwin 2026-01-05T12:26:18Z 2022 The Exponential Map for Hopf Algebras. Ghaliah Alhamzi and Edwin Beggs. SIGMA 18 (2022), 017, 17 pages 1815-0659 2020 Mathematics Subject Classification: 16T05; 46L87; 58B32 arXiv:2203.04549 https://nasplib.isofts.kiev.ua/handle/123456789/211528 https://doi.org/10.3842/SIGMA.2022.017 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 ∗-bimodule of 1/2 densities, and elements of the dual Hopf algebra. We give examples for complex-valued functions on the groups ₃ and ℤ, Woronowicz's matrix quantum group ℂq[₂], and the Sweedler-Taft algebra. We would like to thank the editor and referees for many useful comments. Computer algebra and graphs were done on Mathematica. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Exponential Map for Hopf Algebras Article published earlier |
| spellingShingle | The Exponential Map for Hopf Algebras Alhamzi, Ghaliah Beggs, Edwin |
| title | The Exponential Map for Hopf Algebras |
| title_full | The Exponential Map for Hopf Algebras |
| title_fullStr | The Exponential Map for Hopf Algebras |
| title_full_unstemmed | The Exponential Map for Hopf Algebras |
| title_short | The Exponential Map for Hopf Algebras |
| title_sort | exponential map for hopf algebras |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211528 |
| work_keys_str_mv | AT alhamzighaliah theexponentialmapforhopfalgebras AT beggsedwin theexponentialmapforhopfalgebras AT alhamzighaliah exponentialmapforhopfalgebras AT beggsedwin exponentialmapforhopfalgebras |