Hypercomplex systems and representations

Operator groups, semisimple rings and representations lead to central simple algebras, crossed products, Galois descent and the principal genus theorem. The final arithmetic lesson separates its proved reductions from its stated class-field-theory inputs.

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 (in preparation)
5. Crossed products and factor systems (in preparation)
6. Hilbert 90 in Noether's form and Galois descent (in preparation)
7. The principal genus theorem (in preparation)

Original text CC0 1.0 unless the lesson states other terms.

Further lessons

• Hilbert 90 in Noether's form and Galois descent