Lecture

Geometric McKay correspondence: Du Val singularities and Dynkin diagrams

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In course

MATH-335: Coxeter groups

Study groups generated by reflections ...

Description

This lecture explores the derivation of simply laced Dynkin diagrams from the geometric properties of Du Val singularities in C^2/Gamma, where Gamma is a finite subgroup of SU(2). The slides cover topics such as the definition of singular points, resolution of singularities, blow-up of C^2, and the relationship between Du Val singularities and Dynkin graphs.

Instructor

Anna Lachowska

Teaching & PhD Courses Algebra MATH-310 This is an introduction to modern algebra: groups, rings and fields. Analysis I MATH-101(e) We study the fundamental concepts of analysis, calculus and the integral of real-valued functions of a real variable. Analysis II MATH-106(e) The course studies fundamental concepts of analysis and the calculus of functions of several variables. Representation theory I - finite groups MATH-314 This is a standard c

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Lexical definition

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Finitely generated group

In algebra, a finitely generated group is a group G that has some finite generating set S so that every element of G can be written as the combination (under the group operation) of finitely many elements of S and of inverses of such elements. By definition, every finite group is finitely generated, since S can be taken to be G itself. Every infinite finitely generated group must be countable but countable groups need not be finitely generated. The additive group of rational numbers Q is an example of a countable group that is not finitely generated.

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