Affine, Vertex and W-algebras

This book focuses on recent developments in the theory of vertex algebras, with particular emphasis on affine vertex algebras, affine W-algebras, and W-algebras appearing in physical theories such as logarithmic conformal field theory. It is widely accepted in the mathematical community that the best way to study the representation theory of affine Kac–Moody algebras is by investigating the representation theory of the associated affine vertex and W-algebras. In this volume, this general idea can be seen at work from several points of view. Most relevant state of the art topics are covered, including fusion, relationships with finite dimensional Lie theory, permutation orbifolds, higher Zhu algebras, connections with combinatorics, and mathematical physics. The volume is based on the INdAM Workshop Affine, Vertex and W-algebras, held in Rome from 11 to 15 December 2017. It will be of interest to all researchers in the field.

Dražen Adamovic  is Full Professor of Mathematics  at the University of Zagreb, Croatia. He received his PhD in Mathematics from the University of Zagreb. He is the author of more than 50 peer-reviewed research publications on the representation theory of vertex algebras, W-algebras, and infinite-dimensional Lie algebras, with special emphasis on vertex algebras appearing in conformal field theory.

Paolo Papi is Full Professor of Geometry at Sapienza University of Rome, Italy. He received his PhD in Mathematics from the University of Pisa. He is the author of more than 40 peer-reviewed research publications on Lie theory, algebraic combinatorics, representation theory of Lie algebras, and superalgebras, with special emphasis on combinatorics of root systems and infinite dimensional structures (affine Lie algebras, vertex algebras).