Title: Analytic<i>H</i>-spaces, Campbell-Hausdorff formula, and alternative algebras
Abstract: Analytic //-spaces are shown to be local analytic loops (satisfying the cancellation laws).Then power associative local analytic loops are investigated and these are shown to be exactly the class to which a local loop belongs if there is a choice of coordinate system, /, for which the multiplication obeys V(sx 9 tx) -sx + tx.Here x is near 0 in R n , each of the numbers 5, t and 5 + / is in [0,1] and V is the pulldown of the local loop multiplication via /.Homomorphism of such local loops are investigated and the set of such automorphism is shown to be isomorphic to a certain group of linear maps.Also generalizing the Lie group-Lie algebra situation, certain anti-commutative algebras are introduced to study these local loops.Finally these results are applied to local loops whose multiplication is induced by a power associative algebra.A Campbell-Hausdorff formula is shown to hold when the algebra is alternative and is related to the inverse property in the local loop.A relationship between S 7 and simple Malcev algebras is given.