**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.

Lecture# Decomposition of Group Algebras

Description

This lecture covers examples of decomposition of group algebras into a direct sum of matrix algebras, the group algebra of a finite group as a left module over itself, and the concept of a simple infinite-dimensional algebra, specifically the Weyl algebra over a field of zero characteristic. The lecture also discusses theorems related to simple modules, such as Wedderburn's and Maschke's theorems, and provides examples of group algebras as left modules over themselves. Additionally, it explores the structure of the Weyl algebra, its basis, and its properties as a simple algebra that is not a matrix algebra. The lecture concludes with the study of tensor products in the context of group algebras.

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

In course

DEMO: occaecat aliquip

Anim consectetur in labore id qui culpa velit commodo eiusmod pariatur occaecat incididunt exercitation minim. Proident reprehenderit cupidatat Lorem irure et nulla in do. Nulla eiusmod ut eiusmod aute Lorem laboris sint consequat. Ex labore quis consectetur sunt ipsum aliquip sit. Cillum do est laborum laboris non. Ullamco irure sint deserunt reprehenderit occaecat ad cupidatat tempor ea.

Ontological neighbourhood

Related lectures (103)

Group Algebra: Maschke's Theorem

Explores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.

Weyl character formula

Explores the proof of the Weyl character formula for finite-dimensional representations of semisimple Lie algebras.

Ideals and Representations

Covers ideals, representations, modules, and maximal ideals in associative algebras.

Group Cohomology

Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.

Simple Modules: Schur's Lemma

Covers simple modules, endomorphisms, and Schur's lemma in module theory.