In mathematics, an isotopy from a possibly non-associative algebra A to another is a triple of bijective linear maps (a, b, c) such that if xy = z then a(x)b(y) = c(z).
This is similar to the definition of an isotopy of loops, except that it must also preserve the linear structure of the algebra.
Isotopy of algebras was introduced by Albert (1942), who was inspired by work of Steenrod.
Some authors use a slightly different definition that an isotopy is a triple of bijective linear maps a, b, c such that if xyz = 1 then a(x)b(y)c(z) = 1.
For alternative division algebras such as the octonions the two definitions of isotopy are equivalent, but in general they are not.