Mutation (algebra)

In specific cases the resulting algebra may be referred to as a homotope or an isotope of the original.

Let A be an algebra over a field F with multiplication (not assumed to be associative) denoted by juxtaposition.

to be the algebra with multiplication Similarly define the left (a,b) mutation

[1] If A is a unital algebra and a is invertible, we refer to the isotope by a.

The Jordan triple product is defined by For y in A the mutation[3] or homotope[4] Ay is defined as the vector space A with multiplication and if y is invertible this is referred to as an isotope.