Noncommutative Algebra - Fall 2020

Instructor

• jthartwig.net

Texts

• McConnell-Robson, Noncommutative Noetherian Rings
• Jacobson, Basic algebra I and II
• Lenagan-Krause, GK dimension
• Lorenz, A Tour of Representation Theory
• Bergman, Diamond Lemma for Ring Theory (Sections 1, 2.1, 3)
• Chase-Harrison-Rosenberg

Topics

• Presentations of algebras; construction of homomorphisms
• Adjoining generators, universal property, relations
• The Diamond Lemma
• Skew polynomial rings and Ore extensions
• Generalized Weyl algebras
• Tensor products; Tensor-Hom adjunction
• Clifford theory for crossed products
• Morita equivalence
• Filtered and associated graded algebras; Poisson algebras
• Gelfand-Kirillov dimension

Lecture Notes

1. Algebras and Modules
2. Adjoining generators
3. Presentations of Algebras
4. Skew polynomial rings and Ore extensions
5. Adjunctions, derivations, and GWAs
6. More about GWAs
7. Degree derivations and graded ideals
8. Filtered algebras
9. The rational Cherednik algebras
10. The Diamond Lemma 1
11. The Diamond Lemma 2
12. The Diamond Lemma 3
13. Group-graded algebras
14. Tensor products 1
15. Tensor products 2
16. Some induced modules
17. Morita equivalence
18. Morita for skew group algebras
19. Clifford theory I
20. Example of Clifford idea
21. Growth of algebras 1
22. Growth of algebras 2
23. Growth of algebras 3
24. Growth of algebras 4
25. Quantum algebras
26. Limit topology
27. Deformation theory

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