Representation of an algebra associated with the Dynkin graph $\tilde E_7$
We describe the structure of pairs of self-adjoint operators $A$ and $B$ whose spectra belong to the set $\{±1/2, ±3/2\}$ and for which $(A+B)^2 = I$. Such pairs of operators determine a representation of a *-algebra $A_{\tilde E_7 }$ associated with the extended Dynkin graph $\tilde E_7$.
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| Datum: | 2004 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Ukrainisch Englisch |
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Institute of Mathematics, NAS of Ukraine
2004
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/3835 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860509967547629568 |
|---|---|
| author | Ostrovskii, V. L. Островський, В. Л. |
| author_facet | Ostrovskii, V. L. Островський, В. Л. |
| author_sort | Ostrovskii, V. L. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:12:11Z |
| description | We describe the structure of pairs of self-adjoint operators $A$ and $B$ whose spectra belong to the set $\{±1/2, ±3/2\}$ and for which $(A+B)^2 = I$. Such pairs of operators determine a representation of a *-algebra $A_{\tilde E_7 }$ associated with the extended Dynkin graph $\tilde E_7$. |
| first_indexed | 2026-03-24T02:49:31Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-3835 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T02:49:31Z |
| publishDate | 2004 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/70/ce1f2b1bc93eebf813c2e7e45b4b1f70.pdf |
| spelling | umjimathkievua-article-38352020-03-18T20:12:11Z Representation of an algebra associated with the Dynkin graph $\tilde E_7$ Зображення алгебри, асоційованої з графом Дипкіпа $\tilde E_7$ Ostrovskii, V. L. Островський, В. Л. We describe the structure of pairs of self-adjoint operators $A$ and $B$ whose spectra belong to the set $\{±1/2, ±3/2\}$ and for which $(A+B)^2 = I$. Such pairs of operators determine a representation of a *-algebra $A_{\tilde E_7 }$ associated with the extended Dynkin graph $\tilde E_7$. Описано структуру пар самоспряжепих операторі» А, В, спектр яких міститься в множині {±1/2, ± 3 / 2 } і для яких $(A+B)^2 = I$. Такі пари операторів задають зображення *-алгебри $A_{\tilde E_7 }$, асоційованої з розширеним графом Дипкіна $\tilde E_7$. Institute of Mathematics, NAS of Ukraine 2004-09-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/3835 Ukrains’kyi Matematychnyi Zhurnal; Vol. 56 No. 9 (2004); 1193–1202 Український математичний журнал; Том 56 № 9 (2004); 1193–1202 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/3835/4389 https://umj.imath.kiev.ua/index.php/umj/article/view/3835/4390 Copyright (c) 2004 Ostrovskii V. L. |
| spellingShingle | Ostrovskii, V. L. Островський, В. Л. Representation of an algebra associated with the Dynkin graph $\tilde E_7$ |
| title | Representation of an algebra associated with the Dynkin graph $\tilde E_7$ |
| title_alt | Зображення алгебри, асоційованої з графом Дипкіпа $\tilde E_7$ |
| title_full | Representation of an algebra associated with the Dynkin graph $\tilde E_7$ |
| title_fullStr | Representation of an algebra associated with the Dynkin graph $\tilde E_7$ |
| title_full_unstemmed | Representation of an algebra associated with the Dynkin graph $\tilde E_7$ |
| title_short | Representation of an algebra associated with the Dynkin graph $\tilde E_7$ |
| title_sort | representation of an algebra associated with the dynkin graph $\tilde e_7$ |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/3835 |
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