ON SPECIAL CLASSES OF N-ALGEBRAS

We define n-algebras as linear spaces on which the internal compositio n law involves n elements: m: V(xn)double right arrow V. It is known t hat such algebraic structures are interesting for their applications t o problems of modern mathematical physics. Using the notion of a commu tant of two subalgebras of an n-algebra, we distinguish certain classe s of n-algebras with reasonable properties: semisimple, Abelian, nilpo tent, solvable. We also consider a few examples of n-algebras of diffe rent types, and show their properties. (C) 1996 American Institute of Physics.