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Introduction to Lie Groups Autumn 2020

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Topological groups and Haar measure. Definition of Lie groups, examples of local fields and examples of discrete subgroups; basic properties; Lie subgroups. Lie algebras and relation with Lie groups: exponential map, adjoint representation. Semisimplicity, nilpotency, solvability, compactness: Killing form, Lie's and Engel's theorems. Definition of algebraic groups and relation with Lie groups. The goal is to have a broad though foundational knowledge of the theory of Lie groups and their associated Lie algebras with an emphasis on the algebraic and topological aspects of it. Topology and basic notions of measure theory. A basic understanding of the concepts of manifold, tangent space and vector field is useful, but could also be achieved throughout the semester. A detailed syllabus will be made available here. The exercise sheets will be released below. More challenging exercises are indicated by † †. The general rule is that exercise sheet 𝑘 k will be released on Thursday of week

Introduction to Lie Groups Autumn 2020 Introduction to Lie Groups Autumn 2020 Lecturer Prof. Dr. Alessandra Iozzi Coordinator Yannick Krifka (E-mail) Content Description Topological groups and Haar measure. Definition of Lie groups, examples of local fields and examples of discrete subgroups; basic properties; Lie subgroups. Lie algebras and relation with Lie groups: exponential map, adjoint representation. Semisimplicity, nilpotency, solvability, compactness: Killing form, Lie's and Engel's theorems. Definition of algebraic groups and relation with Lie groups. Goal The goal is to have a broad

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