Inner automorphisms of Lie algebras related with generic \(2\times 2\) matrices

• Date: 2018
• Main Authors: Drensky, Vesselin, Fındık, Şehmus
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: free Lie algebras; generic matrices; inner automorphisms,Baker-Campbell-Hausdorff formula; 17B01; 17B30; 17B40; 16R30
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/711
• Journal Title: Algebra and Discrete Mathematics

Let \(F_m=F_m(\text{var}(sl_2(K)))\) be the relatively free algebra of rank \(m\) in the variety of Lie algebras generated by the algebra \(sl_2(K)\) over a field \(K\) of characteristic 0. Translating an old result of Baker from 1901 we present a multiplication rule for the inner automorphisms of t...