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
• 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
• 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
• 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