Modern Trends in Algebra and Representation Theory

Aimed at graduate students and non-experts, this text gives a guided tour of modern developments in algebra and representation theory.

David Jordan (Edited by), Nadia Mazza (Edited by), Sibylle Schroll (Edited by)

9781009097352, Cambridge University Press

Paperback / softback, published 17 August 2023

430 pages
22.9 x 15.2 x 2.1 cm, 0.58 kg

Expanding upon the material delivered during the LMS Autumn Algebra School 2020, this volume reflects the fruitful connections between different aspects of representation theory. Each survey article addresses a specific subject from a modern angle, beginning with an exploration of the representation theory of associative algebras, followed by the coverage of important developments in Lie theory in the past two decades, before the final sections introduce the reader to three strikingly different aspects of group theory. Written at a level suitable for graduate students and researchers in related fields, this book provides pure mathematicians with a springboard into the vast and growing literature in each area.

Introduction David Jordan, Nadia Mazza and Sibylle Schroll
1. Auslander-Reiten theory of finite-dimensional algebras Raquel Coelho Simões
2. au-Tilting theory – an introduction Hipolito Treffinger
3. From frieze patterns to cluster categories Matthew Pressland
4. Infinite-dimensional representations of algebras Rosanna Laking
5. The Springer correspondence Sam Gunningham
6. An introduction to diagrammatic Soergel bimodules Amit Hazi
7. A companion to quantum groups Bart Vlaar
8. Infinite-dimensional Lie algebras and their multivariable generalizations Brian Williams
9. An introduction to crowns in finite groups Gareth Tracey
10. An introduction to totally disconnected locally compact groups and their finiteness conditions Ilaria Castellano
11. Locally analytic representations of p-adic groups Andreas Bode and Nicolas Dupré.

Subject Areas: Algebra [PBF]