Structure of Group Rings and the Group of Units of Integral Group Rings - Lecture 1
International Centre for Theoretical Sciences via YouTube
Overview
Syllabus
Structure of groups rings and the group of units of integral group rings
Group Ring
What is Group Ring?
Ring theory
Idempotent
What is the idea of a group ring originally?
How does it relate to this as groups isomorphic?
What are the invertible elements?
Lemma
Why these problems are equivalent?
Augmentation mapping
Why the unit group is really relevant?
Does that exist a torsion free normal subgroup say N, of UnZG ?
Black box
Via braces one gets closer and closer to this and braces are solutions of young Baxter equation
Why to look at unit groups?
Constructions of units
Unipotent unit
Construct potent element from idempotent
Notation
Bass units
Number theory
Cyclotomic units
Theorem
Taught by
International Centre for Theoretical Sciences