Non-associative normed algebras and hurwitz' problem

Non Associative Linear Algebras

Non-associative algebras associated to Poisson algebras

Poisson algebras are usually defined as structures with two operations, a commutative associative one and an anti-commutative one that satisfies the Jacobi identity. These operations are tied up by a distributive law, the Leibniz rule. We present Poisson algebras as algebras with one operation, which enables us to study them as part of non-associative algebras. We study the algebraic and cohomo...

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...

Dimension Computations in Non-Commutative Associative Algebras