Lecture in Pairs: Filtered-Graded Transfer and PBW Deformations

 

Content

• algebraic structures (from magmas to finitely presented associative rings), examples of important rings and algebras
• gradings, properties of graded rings, graded modules
• algorithmic aspects, noncommutative factorization
• filtrations, associated grading, filtered-graded transfer of ring-theoretic properties (like theorems of Jacobson), "meta-theorem"
• Krull dimension over commutative rings, properties, connection to Hilbert-Poincare series of rings and modules
• Gel'fand-Kirillov dimension (GKdim) over K-algebras, properties, extension beyond finitely presented case, GKdim over commutative algebras, comparison with the Krull dimension
• PBW deformations
• applications