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.
Papildus informācija
Aimed at graduate students and non-experts, this text gives a guided tour of modern developments in algebra and representation theory.
Introduction David Jordan, Nadia Mazza and Sibylle Schroll;
1.
Auslander-Reiten theory of finite-dimensional algebras Raquel Coelho Simões;
2. -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.
