Structure theorems for families of idempotents
For *-algebras generated by idempotents and orthoprojectors, we study the complexity of the problem of description of *-representations to within unitary equivalence. In particular, we prove that the *-algebra generated by two orthogonal idempotents is *-wild as well as the *-algebra generated by th...
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| Datum: | 1998 |
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| Hauptverfasser: | , , , |
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| Sprache: | Russisch Englisch |
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Institute of Mathematics, NAS of Ukraine
1998
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/4922 |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511109951258624 |
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| author | Kruhlyak, S. A. Samoilenko, Yu. S. Кругляк, С. А. Самойленко, Ю. С. Кругляк, С. А. Самойленко, Ю. С. |
| author_facet | Kruhlyak, S. A. Samoilenko, Yu. S. Кругляк, С. А. Самойленко, Ю. С. Кругляк, С. А. Самойленко, Ю. С. |
| author_sort | Kruhlyak, S. A. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:17:16Z |
| description | For *-algebras generated by idempotents and orthoprojectors, we study the complexity of the problem of description of *-representations to within unitary equivalence. In particular, we prove that the *-algebra generated by two orthogonal idempotents is *-wild as well as the *-algebra generated by three orthoprojectors, two of which are orthogonal. |
| first_indexed | 2026-03-24T03:07:40Z |
| format | Article |
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| id | umjimathkievua-article-4922 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:07:40Z |
| publishDate | 1998 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/1a/8155258eea8e3ccc6659a6cf3992ee1a.pdf |
| spelling | umjimathkievua-article-49222020-03-18T21:17:16Z Structure theorems for families of idempotents Структурные теоремы для семейств идемпотентов Kruhlyak, S. A. Samoilenko, Yu. S. Кругляк, С. А. Самойленко, Ю. С. Кругляк, С. А. Самойленко, Ю. С. For *-algebras generated by idempotents and orthoprojectors, we study the complexity of the problem of description of *-representations to within unitary equivalence. In particular, we prove that the *-algebra generated by two orthogonal idempotents is *-wild as well as the *-algebra generated by three orthoprojectors, two of which are orthogonal. Для *-алгебр, породжених ідемпотентами та ортопроекторами, вивчається складність задачі опису *-зображень з точністю до унітарної еквівалентності. Зокрема, доводиться, що *-алгебра, породжена двома ортогональними ідемпотентами, та *-алгебра, породжена трьома ортопроекторами, два з яких ортогональні, є *-дикими. Institute of Mathematics, NAS of Ukraine 1998-04-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4922 Ukrains’kyi Matematychnyi Zhurnal; Vol. 50 No. 4 (1998); 523–533 Український математичний журнал; Том 50 № 4 (1998); 523–533 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4922/6543 https://umj.imath.kiev.ua/index.php/umj/article/view/4922/6544 Copyright (c) 1998 Kruhlyak S. A.; Samoilenko Yu. S. |
| spellingShingle | Kruhlyak, S. A. Samoilenko, Yu. S. Кругляк, С. А. Самойленко, Ю. С. Кругляк, С. А. Самойленко, Ю. С. Structure theorems for families of idempotents |
| title | Structure theorems for families of idempotents |
| title_alt | Структурные теоремы для семейств идемпотентов |
| title_full | Structure theorems for families of idempotents |
| title_fullStr | Structure theorems for families of idempotents |
| title_full_unstemmed | Structure theorems for families of idempotents |
| title_short | Structure theorems for families of idempotents |
| title_sort | structure theorems for families of idempotents |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4922 |
| work_keys_str_mv | AT kruhlyaksa structuretheoremsforfamiliesofidempotents AT samoilenkoyus structuretheoremsforfamiliesofidempotents AT kruglâksa structuretheoremsforfamiliesofidempotents AT samojlenkoûs structuretheoremsforfamiliesofidempotents AT kruglâksa structuretheoremsforfamiliesofidempotents AT samojlenkoûs structuretheoremsforfamiliesofidempotents AT kruhlyaksa strukturnyeteoremydlâsemejstvidempotentov AT samoilenkoyus strukturnyeteoremydlâsemejstvidempotentov AT kruglâksa strukturnyeteoremydlâsemejstvidempotentov AT samojlenkoûs strukturnyeteoremydlâsemejstvidempotentov AT kruglâksa strukturnyeteoremydlâsemejstvidempotentov AT samojlenkoûs strukturnyeteoremydlâsemejstvidempotentov |