Algebraic Bol loops

作者：Grishkov Alexander^*; Nagy Gabor P

来源：Forum Mathematicum, 2011, 23(3): 655-668.

DOI：10.1515/FORM.2011.032

• Bol loops
• algebraic loops
• simple loops
• algebraic groups as multiplication groups
• local algebraic loops

In this paper, we study the category of algebraic Bol loops over an algebraically closed field of definition. On the one hand, we apply techniques from the theory of algebraic groups in order to prove structural theorems for this category. On the other hand, we present some examples showing that these loops lack some nice properties of algebraic groups; for example, we construct local algebraic Bol loops which are not birationally equivalent to global algebraic loops.

• 出版日期2011-5