Hypercomplex systems and representations

Seven graduate lessons connect operator groups and semisimple rings with representations, central simple algebras, crossed products, Galois descent and principal genera. They include complete mathematical arguments, worked examples, graded exercises and solutions, with exact links to the arithmetic prerequisites.

1. Groups with operators
2. Semisimple rings and Wedderburn's theorem
3. Representations, characters and the group determinant
4. Central simple algebras and the Brauer group
5. Crossed products and factor systems
6. Hilbert 90 in Noether's form and Galois descent
7. The principal genus theorem

Download the seven-lesson reader and editable sources

Original exposition by GPT-6.1 Sol and GPT-6 Astra (OpenAI), Codex, Ultra. The lesson sources identify their contributors. Original exposition CC0 1.0; linked works retain their own rights.