In a connected group of finite Morley rank in which the generic element belongs to a connected nilpotent subgroup, proper normalizing cosets of definable subgroups are not generous. We explain why this is true and what consequences this has on an abstract theory of Weyl groups in groups of finite Morley rank. The only known infinite simple groups of finite Morley rank are the simple algebraic g...

We consider normalizers of an irreducible inclusion N ⊆ M of II1 factors. In the infinite index setting an inclusion uNu∗ ⊆ N can be strict, forcing us to also investigate the semigroup of one-sided normalizers. We relate these normalizers of N in M to projections in the basic construction and show that every trace one projection in the relative commutant N ′ ∩ 〈M, eN 〉 is of the form ueNu for ...

A bstract In recent years it has been understood that new rational CFTs can be discovered by applying the coset construction to meromorphic CFTs. Here we turn this approach around and show construction, together with classification of CFT c ? 24, used predict existence ? 32 whose Kac-Moody algebras are non-simply-laced and/or at levels greater than 1. This implies they non-lattice theories. Usi...