Syllabus

  Date   Topics Sections Recommended Exercises for Further Practice
Jan 8 Associative algebras: representations, examples. GW 4.1.1 4.1.8: 5, 6.
Jan 11 Schur's Lemma, Jacobson's density theorem. GW 4.1.2–4.1.3  
Jan 15 Burnside's theorem, complete reducibility of A-modules, tensor product of vector spaces and algebras. GW 4.1.3–4.1.4 4.1.8: 1(a), 1(b).
Jan 18 Double commutant theorem, isotypic decompositions and multiplicities, characters of A-modules. GW 4.1.5–4.1.7  
Jan 22 General duality theorem. GW 4.2.1 4.2.7: 1, 2.
Jan 25 Schur-Weyl duality - abstract form
First Assignment
GW 4.2.4  
Jan 29 Schur-Weyl duality - abstract form (continued), superalgebras. GW 4.2.4, CW 3.1.1  
Feb 1 The super tensor product, classification of simple superalgebras. CW 3.1.1  
Feb 5 Classification of simple superalgebras, semisimple superalgebras. CW 3.1.1–3.1.2  
Feb 8 Characterization of semisimple superalgebras. CW 3.1.2  
Feb 12 Characterization of semisimple superalgebras, Schur's Lemma for superalgebras. CW 3.1.2  
Feb 15 Example: finite supergroups.
Second Assignment
CW 3.1.4  
Feb 19 Reading Week      
Feb 22 Reading Week      
Feb 26 Structure theory for gln; root systems and Borel subalgebras.    
Mar 1 Midterm Exam      
Mar 5 Highest weight theory for gln.    
Mar 8      
Mar 12      
Mar 15  
Third Assignment
   
Mar 19      
Mar 22      
Mar 26      
Mar 29      
Apr 2      
Apr 5 Presentations
Fourth Assignment
     
Apr 9 Presentations