Group Algebras

A group algebra may be created for a finite group of moderate order over a Euclidean Domain.

• Creation of group algebras: a vector and term representation are provided allowing the construction of algebras for groups of arbitrary size.
• Arithmetic including Lie bracket operation
• Properties of elements: idempotent, unit, zero-divisor, nilpotent
• Trace and minimal polynomial
• Creation of subalgebras, ideals and quotient algebras
• Ideal arithmetic: Sum, product, powers, intersection
• Centralizer, idealizer
• Augmentation ideal, augmentation map
• Characteristic ideals: Centre, commutator ideal, Jacobson radical
• Ideal structure: Maximal (minimal) left, right, two-sided ideals
• Decomposition: Simplicity, semi-simplicity, composition series
• Construction of the (left, right) regular matrix representation