Algebras#

Algebras

Overview, creation, substructures and general operations on algebras.

Structure Constant Algebras

Algebras defined by structure constants.

Associative Algebras

Structure, subalgebras, ideals and the Jacobson radical.

Finitely Presented Algebras

Algebras given by generators and relations.

Matrix Algebras

Matrix algebras: creation, substructures and extensions.

Group Algebras

Group algebras: creation, substructures and element operations.

Basic Algebras

Basic algebras, gradings, idempotents and their homomorphisms.

Quaternion Algebras

Quaternion algebra constructors, maximal orders and splitting.

Algebras with Involution

Star algebras, involutions and their decompositions.

Clifford Algebras

Clifford algebras, involutions and spin groups.

Non-associative Algebras

Jordan algebras, alternative algebras and octonions.