ABOUT NONASSOCIATIVITY IN MATHEMATICS AND PHYSICS

A short review about nonassociative algebraic systems (mainly nonassoc iative algebras) and their physical applications is presented. We begi n with some motivations, then we give a brief historical overview abou t the formation and development of the concept of hypercomplex number system and about some earlier applications. The main directions discus sed are the octonionic, Lie-admissible, and quasigroup approaches. Als o, some problems investigated in Tartu, the octonionic approach, Moufa ng-Mal'tsev symmetry, and associator quantization are discussed. This review does not pretend to be complete as the accent is placed on idea s and not on the techniques, also the references are quite sporadic (t here are many authors and results mentioned in the text without refere nces).