The First Cohomology Group of a Line Bundle on G/B.
A loop is automorphic if all its inner mappings are automorphisms. We construct the free commutative automorphic -generated loop of nilpotency class . It has dimension over the integers.
The left distributive law is the law a· (b· c) = (a·b) · (a· c). Left distributive algebras have been classically used in the study of knots and braids, and more recently free left distributive algebras have been studied in connection with large cardinal axioms in set theory. We provide a survey of results on the free left distributive algebra on one generator, A, and a new, simplified proof of the existence of a normal form for terms in A. Topics included are: the confluence of A, the linearity...
The full automorphism group of the Kulkarni surface is explicitly determined. It is employed to give three defining equations of the Kulkarni surface; each equation exhibits a symmetry of the surface as complex conjugation.