The universality of one half in commutative nonassociative algebras with identities

Nonassociative Algebras

Non-Commutative Elimination in Ore Algebras Proves Multivariate Identities

Many identities involving special functions, combinatorial sequences or their q-analogues can be proved using linear operators and simple arguments on the dimension of related vector spaces. In this article, we develop a theory of @-nite sequences and functions which provides a uniied framework to express algorithms proving and discovering mul-tivariate identities. This approach is vindicated b...

On Nonassociative Division Algebras^)

Nonassociative Algebras with Submultiplicative Bilinear Form

In this paper algebras with identity, over ordered fields, which possess a (weak) submultiplicative positive bilinear form are studied. They are called (weak) subdecomposition algebras. It is proved that every weak subdecomposition algebra is a simple quadratic algebra with no nontrivial nilpotents or idempotents. If a weak subdecomposition algebra is also flexible, then it is a noncommutative ...

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.