Decomposition of matrices from \(\text{SL}_{2}(\mathbb{K}[x, y])\)

• Datum: 2025
• Hauptverfasser: Chapovskyi, Yevhenii, Kozachok, Oleksandra, Petravchuk, Anatoliy
• Format: Artikel
• Sprache: English
• Veröffentlicht: Lugansk National Taras Shevchenko University 2025
• Schlagworte: row; special linear group; generators; decomposition
• Online Zugang: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2362
• Назва журналу: Algebra and Discrete Mathematics

Let \(\mathbb{K}\) be an algebraically closed field of characteristic zero and \(\mathbb{K}[x, y]\) the polynomial ring. The group \(\text{SL}_{2}(\mathbb{K}[x, y])\) of all matrices with determinant equal to \(1\) over \(\mathbb{K}[x, y]\) can not be generated by elementary matrices. The known coun...