BN-pairs and groups of finite Morley rankJosh Wiscons, CU |
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December 9 AbstractThe class of groups of finite Morley rank consists of groups that can be equipped with a (model theoretic) notion of dimension, called Morley rank, that applies to the definable subsets of the group in much the same way that the notion of dimension of an algebraic group applies to its constructible sets. In fact, much effort has been put into the Cherlin-Zil'ber conjecture which states that a group of finite Morley rank which is simple is isomorphic (as an abstract group) to an algebraic group over an algebraically closed field. We will discuss how BN-pairs, which have been very helpful in understanding simple algebraic groups, may be helpful in approaching this conjecture. |