Algebraic Combinatorics and the Monster Group [Paperback]

The current state of knowledge on the Monster group, including Majorana theory, Vertex Operator Algebras, Moonshine and maximal subgroups.This text provides the current state of knowledge on, arguably, one of the most attractive and mysterious mathematical objects: the Monster group. Some 20 experts here share their expertise in this exciting field. Ideal for researchers and graduate students working in Combinatorial Algebra, Group theory and related areas.This text provides the current state of knowledge on, arguably, one of the most attractive and mysterious mathematical objects: the Monster group. Some 20 experts here share their expertise in this exciting field. Ideal for researchers and graduate students working in Combinatorial Algebra, Group theory and related areas.Covering, arguably, one of the most attractive and mysterious mathematical objects, the Monster group, this text strives to provide an insightful introduction and the discusses the current state of the field. The Monster group is related to many areas of mathematics, as well as physics, from number theory to string theory. This book cuts through the complex nature of the field, highlighting some of the mysteries and intricate relationships involved. Containing many meaningful examples and a manual introduction to the computer package GAP, it provides the opportunity and resources for readers to start their own calculations. Some 20 experts here share their expertise spanning this exciting field, and the resulting volume is ideal for researchers and graduate students working in Combinatorial Algebra, Group theory and related areas.Part I. The Monster: 1. Lectures on vertex algebras Atsushi Matsuo; 2. 3-Transposition groups arising in vertex operator algebras Hiroshi Yamauchi; 3. On holomorphic vertex operator algebras of central charge 24 Ching Hung Lam; 4. Maximal 2-local subgroups of the Monster and Baby Monster Ulrich Meierfrankenfeld and Sergey Shpectorov; 5. The future of Majorana theory II Alló’