Modern Trends in Algebra and Representation Theory

David Jordan (University of Edinburgh), Nadia Mazza (Lancaster University), Sibylle Schroll (Universität zu Köln)

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English

Cambridge University Press
17 August 2023

Algebra; Groups & group theory; Combinatorics & graph theory

Series: London Mathematical Society Lecture Note Series

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.

Edited by: David Jordan (University of Edinburgh), Nadia Mazza (Lancaster University), Sibylle Schroll (Universität zu Köln)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 229mm, Width: 152mm, Spine: 21mm
Weight: 580g
ISBN: 9781009097352
ISBN 10: 1009097350
Series: London Mathematical Society Lecture Note Series
Pages: 430
Publication Date: 17 August 2023
Audience: College/higher education , Further / Higher Education
Format: Paperback
Publisher's Status: Active

Introduction David Jordan, Nadia Mazza and Sibylle Schroll; 1. Auslander-Reiten theory of finite-dimensional algebras Raquel Coelho Simões; 2. τ-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.

David Jordan is Professor of Categorical Symmetry at the University of Edinburgh. Nadia Mazza is Professor in Pure Mathematics at Lancaster University. Sibylle Schroll is Professor of Mathematics at the University of Cologne and Adjunct Professor at the Norwegian University of Science and Technology.