Low Dimensional A-infinity Algebras

Abstract

Associative algebras (eg. polynomial algebras, complex numbers, matrix algebras) are familiar objects to most students. A-infinity algebras are generalizations of associative algebras which were first studies by topologists in the 1960s but later became important in mathematical physics. Until recently, there have been few concrete examples of such structures. This study examines some low dimensional examples with the aim of developing a classification of A-infinity algebra structures on some low dimensional spaces.