The classification of serial posets with the non-negative quadratic Tits form being principal
Using (introduced by the first author) the method of (min, max)-equivalence, we classify all serial principal posets, i.e. the posets \(S\) satisfying the following conditions: (1) the quadratic Tits form \(q_S(z)\colon\mathbb{Z}^{|S|+1}\to\mathbb{Z}\) of \(S\) is non-negative; (2) \({\rm Ker}\,q...
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| Дата: | 2019 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2019
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1393 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| Резюме: | Using (introduced by the first author) the method of (min, max)-equivalence, we classify all serial principal posets, i.e. the posets \(S\) satisfying the following conditions: (1) the quadratic Tits form \(q_S(z)\colon\mathbb{Z}^{|S|+1}\to\mathbb{Z}\) of \(S\) is non-negative; (2) \({\rm Ker}\,q_S(z):=\{t\,|\, q_S(t)=0\}\) is an infinite cyclic group (equivalently, the corank of the symmetric matrix of \(q_S(z)\) is equal to \(1\)); (3) for any \(m\in\mathbb{N}\), there is a poset \(S(m)\supset S\) such that \(S(m)\) satisfies (1), (2) and \(|S(m)\setminus S|=m\). |
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