Nonassociative normed algebras: geometric aspects

Nonassociative Algebras

On Nonassociative Division Algebras^)

A class of nonassociative algebras

A large class of nonassociative algebras, out of the Lie algebras has been studied, often with geometrical structures and sometimes on fondamental spaces as the spaces of Hochschild cohomology. In this paper, we propose to consider all these nonassociative algebras as algebras defined by the action of invariant subspaces of the symmetric group Σ 3 on the associator of the considered laws.

Notes on normed algebras

All vector spaces and so forth here will be defined over the complex numbers. If z = x+i y is a complex number, where x, y are real numbers, then the complex conjugate of z is denoted z and defined to be x− i y. The complex conjugate of a sum or product of complex numbers is equal to the corresponding sum or product of complex conjugates. The modulus of a complex number z is the nonnegative rea...

Of Normed Algebras In

Let X be a non-degenerate left Banach module over a normed algebra A having a bounded approximate left identity. We show that, if A is a left ideal of a larger algebra, then this representation can be extended to a representation of the larger algebra. Based on this result, we study in detail the existence and properties of representations of the various centralizer algebras of A which are comp...