Nonassociative Algebras with Submultiplicative Bilinear Form

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.

Arens regularity of bilinear forms and unital Banach module spaces

Assume that $A$‎, ‎$B$ are Banach algebras and that $m:Atimes Brightarrow B$‎, ‎$m^prime:Atimes Arightarrow B$ are bounded bilinear mappings‎. ‎We study the relationships between Arens regularity of $m$‎, ‎$m^prime$ and the Banach algebras $A$‎, ‎$B$‎. ‎For a Banach $A‎$‎-bimodule $B$‎, ‎we show that $B$ factors with respect to $A$ if and only if $B^{**}$ is unital as an $A^{**}‎$‎-module‎. ‎Le...

Chevalley Groups of Type G2 as Automorphism Groups of Loops

Let M∗(q) be the unique nonassociative finite simple Moufang loop constructed over GF (q). We prove that Aut(M∗(2)) is the Chevalley group G2(2), by extending multiplicative automorphism of M∗(2) into linear automorphisms of the unique split octonion algebra over GF (2). Many of our auxiliary results apply in the general case. In the course of the proof we show that every element of a split oct...

Structure and Representation of Nonassociative Algebras

Continuity of Derivations on //»-algebras

We prove that the separating subspace for a derivation on a nonassociative //'-algebra is contained in the annihilator of the algebra. In particular, derivations on nonassociative H* -algebras with zero annihilator are continuous.