Irreducible maps and bilinear forms

Abstract

Bautista showed in 1982 that the possible multiplicities of indecomposable summands of the domains and ranges of irreducible maps between modules over artin algebras are given by numerical invariants of certain bilinear forms associated with the algebra. We obtain further information about these multiplicities by relating the forms to those studied elsewhere in algebra and geometry. One spectacular result is that the allowable multiplicities for some algebras over the field of real numbers depend on J.F. Adams’ determination of the number of linearly independent vector fields on a sphere.