Infinite-dimensional Lie Algebras by Iain Gordon
About this book :-
Kac–Moody is a special kind of algebra called algebras, which are important in both mathematics and physics. The book covers how these algebras work, how they can be used, and how they connect to things like number theory and symmetry. Iain Gordon is a mathematician who studies related topics, especially Cherednik algebras, and has taught courses on infinite-dimensional Lie algebras, but he hasn’t written a book with that title.
This text cover The Central extensions, The Virasoro algebra, The Heisenberg algebra, Enveloping algebras, A little infinite-dimensional surprise, Hands-on loop and affine algebras, Simple Lie algebras, Kac-Moody Lie algebras, Classification of generalised Cartanmatrices, Dynkin diagrams, Forms, Weyl groups and roots, Root spaces, Affine Lie algebras and Kac-Moody Lie algebras, etc.
Book Detail :-
Title:
Infinite-dimensional Lie Algebras by Iain Gordon
Publisher:
University of Edinburgh
Year:
2009
Pages:
55
Type:
PDF
Language:
English
ISBN-10 #:
N\A
ISBN-13 #:
N\A
License:
Linked Content Owned by Author
Amazon:
Amazon
About Author :-
The author
Iain Gordon
is a mathematician, Vice-Principal, Professor of Mathematics and Head of School of the School of Mathematics at the University of Edinburgh. His area of research and interested is "noncommutative algebra" and "representation theory and its applications". He is a member of the Edinburgh Hodge Institute, the collective of algebraists, geometers, number theorists and topologists here. He was the Seggie Brown Fellow Archived 31 July 2021 at the Wayback Machine in Edinburgh (1998–99) and a postdoc at the Bielefeld University, the University of Antwerp and MSRI (1999–2000). He was a lecturer and then reader in the Department of Mathematics at the University of Glasgow (2000–2006), and since then has been the Professor of Mathematics at the University of Edinburgh.
Book Contents :-
1. Introduction
2. Central extensions
3. The Virasoro algebra
4. The Heisenberg algebra
5. Representations of the Virasoro algebra
6. Enveloping algebras
7. The universal highest-weight representations of Vir
8. Irreducibilty and unitarity of Virasoro representations
9. A little infinite-dimensional surprise
10. Hands-on loop and affine algebras
11. Simple Lie algebras
12. Kac-Moody Lie algebras
13. Classification of generalised Cartan matrices
14. Dynkin diagrams
15. Forms, Weyl groups and roots
16. Root spaces
17. Affine Lie algebras and Kac-Moody Lie algebras
18. The Weyl-Kac formula
19. W - K + A = M
20. KP hierarchy and Lie theory
21. The Kazhdan-Lusztig Conjecture
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