Minimax equivalence method: initial ideas, first applications and new concepts
In 2005, the author introduced for posets the notion of (min, max)-equivalence (later called minimax equivalence). This equivalence preserves \(\mathbb{Z}\)-equivalence of the corresponding Tits quadratic forms which play an important role in modern representation theory. The minimax equivalence met...
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| Datum: | 2024 |
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| Sprache: | English |
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Lugansk National Taras Shevchenko University
2024
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admjournalluguniveduua-article-23322024-09-23T09:29:11Z Minimax equivalence method: initial ideas, first applications and new concepts Bondarenko, Vitaliy M. positive poset, P-critical poset, minimax equivalence, Tits quadratic form, 0-isomorphism, minimax system of generators 06A07, 11E04 In 2005, the author introduced for posets the notion of (min, max)-equivalence (later called minimax equivalence). This equivalence preserves \(\mathbb{Z}\)-equivalence of the corresponding Tits quadratic forms which play an important role in modern representation theory. The minimax equivalence method has been used to solving many classification problems. This method was first applied in the same year by the author together with his PhD student M. V. Styopochkina for classifying all posets with positive Tits quadratic form and all minimal posets with nonpositive Tits form. These results were often cited, but the corresponding publication is virtually inaccessible. The paper provides them (translated into English) and also the author's new ideas about the minimax equivalence method. Lugansk National Taras Shevchenko University 2024-09-23 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2332 10.12958/adm2332 Algebra and Discrete Mathematics; Vol 38, No 1 (2024) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2332/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2332/1253 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2332/1254 Copyright (c) 2024 Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics |
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|
| datestamp_date |
2024-09-23T09:29:11Z |
| collection |
OJS |
| language |
English |
| topic |
positive poset P-critical poset minimax equivalence Tits quadratic form 0-isomorphism minimax system of generators 06A07 11E04 |
| spellingShingle |
positive poset P-critical poset minimax equivalence Tits quadratic form 0-isomorphism minimax system of generators 06A07 11E04 Bondarenko, Vitaliy M. Minimax equivalence method: initial ideas, first applications and new concepts |
| topic_facet |
positive poset P-critical poset minimax equivalence Tits quadratic form 0-isomorphism minimax system of generators 06A07 11E04 |
| format |
Article |
| author |
Bondarenko, Vitaliy M. |
| author_facet |
Bondarenko, Vitaliy M. |
| author_sort |
Bondarenko, Vitaliy M. |
| title |
Minimax equivalence method: initial ideas, first applications and new concepts |
| title_short |
Minimax equivalence method: initial ideas, first applications and new concepts |
| title_full |
Minimax equivalence method: initial ideas, first applications and new concepts |
| title_fullStr |
Minimax equivalence method: initial ideas, first applications and new concepts |
| title_full_unstemmed |
Minimax equivalence method: initial ideas, first applications and new concepts |
| title_sort |
minimax equivalence method: initial ideas, first applications and new concepts |
| description |
In 2005, the author introduced for posets the notion of (min, max)-equivalence (later called minimax equivalence). This equivalence preserves \(\mathbb{Z}\)-equivalence of the corresponding Tits quadratic forms which play an important role in modern representation theory. The minimax equivalence method has been used to solving many classification problems. This method was first applied in the same year by the author together with his PhD student M. V. Styopochkina for classifying all posets with positive Tits quadratic form and all minimal posets with nonpositive Tits form. These results were often cited, but the corresponding publication is virtually inaccessible. The paper provides them (translated into English) and also the author's new ideas about the minimax equivalence method. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2024 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2332 |
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AT bondarenkovitaliym minimaxequivalencemethodinitialideasfirstapplicationsandnewconcepts |
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2025-12-02T15:39:42Z |
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2025-12-02T15:39:42Z |
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1850411563385618432 |