Algebra III / Introduction to Algebra III

Time and place: Thursdays 1:00-2:30, so far online at NUCT.

Lecture notes: Scanned lecture notes are available at the links below.

• Lecture 1: Introduction and examples.
• Lecture 2: Complete reducibility and semisimplicity.
• Lecture 3: Unitarity of finite dimensional complex representations.
• Lecture 4: Dual representation, tensor product of representations.
• Lecture 5: Extension and restriction of scalars.
• Lecture 6: Schur's lemma and its applications.
• Lecture 7: Character theory for finite groups.
• Lecture 8: Transitive group actions. Schur orthogonality.
• Lecture 9: Six-functor formalism for QCoh([G\X]).
• Lecture 10: Induction and restriction.
• Lecture 11: Representations of symmetric groups.
• Lecture 12: The classical groups.
• Lecture 13: The Peter-Weyl theorem.
• Lecture 14: Smooth manifolds.
• Lecture 15: Lie groups.

Report problems: Please upload solutions to NUCT.

• Problem set 1.
• Problem set 2.
• Problem set 3.
• Problem set 4.
• Problem set 5.
• Problem set 6.
• Problem set 7.
• Problem set 8.
• Problem set 9.
• Problem set 10.
• Problem set 11.
• Problem set 12.
• Problem set 13.
• Problem set 14.