In abstract algebra, a structurable algebra is a certain kind of unital involutive non-associative algebra over a field.
For example, all Jordan algebras are structurable algebras (with the trivial involution), as is any alternative algebra with involution, or any central simple algebra with involution.
An involution here means a linear anti-homomorphism whose square is the identity.
[1] Assume A is a unital non-associative algebra over a field, and
Structurable algebras were introduced by Allison in 1978.
[3] The Kantor–Koecher–Tits construction produces a Lie algebra from any Jordan algebra, and this construction can be generalized so that a Lie algebra can be produced from an structurable algebra.
Moreover, Allison proved over fields of characteristic zero that a structurable algebra is central simple if and only if the corresponding Lie algebra is central simple.
[4] When the base field is algebraically closed over characteristic not 2 or 3, the automorphism group of such an algebra has identity component equal to the simply connected exceptional algebraic group of type E6.