ℤ³₂-Graded Extensions of Lie Superalgebras and Superconformal Quantum Mechanics
Quantum mechanical systems whose symmetry is given by the ℤ³₂-graded version of superconformal algebra are introduced. This is done by finding a realization of a ℤ³₂-graded Lie superalgebra in terms of a standard Lie superalgebra and the Clifford algebra. The realization allows us to map many models...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2021 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2021
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211352 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | ℤ³₂-Graded Extensions of Lie Superalgebras and Superconformal Quantum Mechanics. Shunya Doi and Naruhiko Aizawa. SIGMA 17 (2021), 071, 14 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862684618972463104 |
|---|---|
| author | Doi, Shunya Aizawa, Naruhiko |
| author_facet | Doi, Shunya Aizawa, Naruhiko |
| citation_txt | ℤ³₂-Graded Extensions of Lie Superalgebras and Superconformal Quantum Mechanics. Shunya Doi and Naruhiko Aizawa. SIGMA 17 (2021), 071, 14 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Quantum mechanical systems whose symmetry is given by the ℤ³₂-graded version of superconformal algebra are introduced. This is done by finding a realization of a ℤ³₂-graded Lie superalgebra in terms of a standard Lie superalgebra and the Clifford algebra. The realization allows us to map many models of superconformal quantum mechanics (SCQM) to their ℤ³₂-graded extensions. It is observed that for the simplest SCQM with (1|2) symmetry, there exist two inequivalent ℤ³₂-graded extensions. Applying the standard prescription of conformal quantum mechanics, the spectrum of the SCQMs with the ℤ³₂-graded (1|2) symmetry is analyzed. It is shown that many models of SCQM can be extended to a ℤⁿ₂-graded setting.
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| first_indexed | 2026-03-17T10:24:10Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211352 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-17T10:24:10Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Doi, Shunya Aizawa, Naruhiko 2025-12-30T15:54:09Z 2021 ℤ³₂-Graded Extensions of Lie Superalgebras and Superconformal Quantum Mechanics. Shunya Doi and Naruhiko Aizawa. SIGMA 17 (2021), 071, 14 pages 1815-0659 2020 Mathematics Subject Classification: 17B75; 17B81; 81R12 arXiv:2103.10638 https://nasplib.isofts.kiev.ua/handle/123456789/211352 https://doi.org/10.3842/SIGMA.2021.071 Quantum mechanical systems whose symmetry is given by the ℤ³₂-graded version of superconformal algebra are introduced. This is done by finding a realization of a ℤ³₂-graded Lie superalgebra in terms of a standard Lie superalgebra and the Clifford algebra. The realization allows us to map many models of superconformal quantum mechanics (SCQM) to their ℤ³₂-graded extensions. It is observed that for the simplest SCQM with (1|2) symmetry, there exist two inequivalent ℤ³₂-graded extensions. Applying the standard prescription of conformal quantum mechanics, the spectrum of the SCQMs with the ℤ³₂-graded (1|2) symmetry is analyzed. It is shown that many models of SCQM can be extended to a ℤⁿ₂-graded setting. The authors would like to thank the referees for their valuable comments on the improvement of this paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications ℤ³₂-Graded Extensions of Lie Superalgebras and Superconformal Quantum Mechanics Article published earlier |
| spellingShingle | ℤ³₂-Graded Extensions of Lie Superalgebras and Superconformal Quantum Mechanics Doi, Shunya Aizawa, Naruhiko |
| title | ℤ³₂-Graded Extensions of Lie Superalgebras and Superconformal Quantum Mechanics |
| title_full | ℤ³₂-Graded Extensions of Lie Superalgebras and Superconformal Quantum Mechanics |
| title_fullStr | ℤ³₂-Graded Extensions of Lie Superalgebras and Superconformal Quantum Mechanics |
| title_full_unstemmed | ℤ³₂-Graded Extensions of Lie Superalgebras and Superconformal Quantum Mechanics |
| title_short | ℤ³₂-Graded Extensions of Lie Superalgebras and Superconformal Quantum Mechanics |
| title_sort | ℤ³₂-graded extensions of lie superalgebras and superconformal quantum mechanics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211352 |
| work_keys_str_mv | AT doishunya z32gradedextensionsofliesuperalgebrasandsuperconformalquantummechanics AT aizawanaruhiko z32gradedextensionsofliesuperalgebrasandsuperconformalquantummechanics |