The classification of serial posets with the non-negative quadratic Tits form being principal

• Date: 2019
• Main Authors: Bondarenko, Vitaliy M., Styopochkina, Marina V.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2019
• Subjects: quiver; serial poset; principal poset; quadratic Tits form; semichain; minimax equivalence; one-side and two-side sums; minimax sum; 15B33; 15A30
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1393
• Journal Title: Algebra and Discrete Mathematics

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...