algebra over a field
vector space equipped with a bilinear product
alternative algebra
abstract algebra with alternative multiplication
hyperbolic quaternion
unital nonassociative algebra over the real numbers generated by generators 𝑖, 𝑗, 𝑘 that mutually anticommute and each square to +1
Dual-complex number
four-dimensional algebra over the real numbers
Dual quaternion
eight-dimensional algebra over the real numbers
geometric algebra
algebraic structure designed for geometry
dual number
algebra over a field
division algebra
algebra over a field with only invertible elements and zero
operator algebra
branch of functional analysis
groupoid algebra
generalization of a group algebra; special case of a category algebra
quasi-Lie algebra
generalization of a Lie algebra, where alternativity is weakened to antisymmetry; equivalent to Lie algebras in characteristics other than 2, but not in characteristic 2
Leibniz algebra
module over a commutative ring with a bilinear product [–, –] such that for any element x, [–, x] is a derivation
Griess algebra
commutative non-associative algebra on a real vector space of dimension 196884 that has the monster group as its automorphism group