Cluster Algebras and Cluster Categories via Surfaces

von Karin Baur

178 Seiten, Hardcover

Kurzbeschreibung des Verlags

Cluster algebras have been introduced by S. Fomin and A. Zelevinsky in the early 2000s, motivated by phenomena observed in the study of (dual) canonical bases of quantised universal enveloping algebras and totally positive matrices. Twenty years of research in cluster theory have established deep links between cluster algebras, surface geometry and representation theory.

These lecture notes give an introduction to the subject which is accessible to graduate students or researchers interested in learning more about the field. The focus is on geometric approaches to cluster algebras and to cluster categories: cluster structures can be defined using combinatorial surface geometry with curves corresponding to cluster variables or to indecomposable objects of cluster categories. Geometric properties like intersections or rotations have interpretations on the cluster algebra side and in the context of cluster categories. The book includes a chapter on frieze patterns and on geometric approaches to module categories. Throughout the text, numerous exercises are presented. The appendix contains background material and hints for the exercises.

• Reihe: Zurich Lectures in Advanced Mathematics
• Themen: Mathematik und Naturwissenschaften Mathematik Algebra
• ISBN: 9783985471171
• Sprache: Englisch
• Erscheinungsdatum: 01.09.2026
• Größe: 24 x 17 cm
• Verlag: EMS Press