List of algebras

This is a list of possibly nonassociative algebras. An algebra is a module, wherein you can also multiply two module elements. (The multiplication in the module is compatible with multiplication-by-scalars from the base ring).


 * *-algebra
 * Affine Lie algebra
 * Akivis algebra
 * Algebra for a monad
 * Albert algebra
 * Alternative algebra
 * AW*-algebra
 * Azumaya algebra
 * Banach algebra
 * Birman–Wenzl algebra
 * Boolean algebra
 * Borcherds algebra
 * Brauer algebra
 * C*-algebra
 * Central simple algebra
 * Clifford algebra
 * Cluster algebra
 * Dendriform algebra
 * Differential graded algebra
 * Differential graded Lie algebra
 * Exterior algebra
 * F-algebra
 * Filtered algebra
 * Flexible algebra
 * Freudenthal algebra
 * Functional-theoretic algebra
 * Genetic algebra
 * Geometric algebra
 * Gerstenhaber algebra
 * Graded algebra
 * Griess algebra
 * Group algebra
 * Group algebra of a locally compact group
 * Hall algebra
 * Hecke algebra of a locally compact group
 * Heyting algebra
 * Hopf algebra
 * Hurwitz algebra
 * Hypercomplex algebra
 * Incidence algebra
 * Iwahori–Hecke algebra
 * Jordan algebra
 * Kac–Moody algebra
 * Kleene algebra
 * Leibniz algebra
 * Lie algebra
 * Lie superalgebra
 * Malcev algebra
 * Matrix algebra
 * Non-associative algebra
 * Octonion algebra
 * Pre-Lie algebra
 * Poisson algebra
 * Process algebra
 * Quadratic algebra
 * Quaternion algebra
 * Rees algebra
 * Relation algebra
 * Relational algebra
 * Rota–Baxter algebra
 * Schur algebra
 * Semisimple algebra
 * Separable algebra
 * Shuffle algebra
 * Sigma-algebra
 * Simple algebra
 * Structurable algebra
 * Supercommutative algebra
 * Symmetric algebra
 * Tensor algebra
 * Universal enveloping algebra
 * Vertex operator algebra
 * von Neumann algebra
 * Weyl algebra
 * Zinbiel algebra

This is a list of fields of algebra.


 * Linear algebra
 * Homological algebra
 * Universal algebra