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Algebraic Bol loops
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Published/Copyright:
April 14, 2010
Abstract
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.
Keywords.: Bol loops; algebraic loops; simple loops; algebraic groups as multiplication groups; local algebraic loops
Received: 2008-05-13
Revised: 2010-02-23
Published Online: 2010-04-14
Published in Print: 2011-May
© de Gruyter 2011
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Articles in the same Issue
- The generalized conjugacy problem for virtually free groups
- Stably diffeomorphic manifolds and l2q+1(ℤ[π])
- The size of the quotient LUC(G)/UC(G)
- Finitistic dimension conjecture and conditions on ideals
- Principal 2-bundles and their gauge 2-groups
- Flat covers over formal triangular matrix rings and minimal Quillen factorizations
- Maximal holonomy of infra-nilmanifolds with 3-dimensional Iwasawa geometry
- Algebraic Bol loops
Keywords for this article
Bol loops;
algebraic loops;
simple loops;
algebraic groups as multiplication groups;
local algebraic loops
Articles in the same Issue
- The generalized conjugacy problem for virtually free groups
- Stably diffeomorphic manifolds and l2q+1(ℤ[π])
- The size of the quotient LUC(G)/UC(G)
- Finitistic dimension conjecture and conditions on ideals
- Principal 2-bundles and their gauge 2-groups
- Flat covers over formal triangular matrix rings and minimal Quillen factorizations
- Maximal holonomy of infra-nilmanifolds with 3-dimensional Iwasawa geometry
- Algebraic Bol loops
