TY  - BOOK
AU  - Hall,J.I.
TI  - Introduction to Lie algebras: finite and infinite dimension 
T2  - Graduate studies in mathematics
SN  - 9781470479152
U1  - 512.55 23
PY  - 2024///
CY  - Providence, Rhode Island
PB  - American Mathematical Society
KW  - Lie algebras
KW  - Kac-Moody algebras
KW  - Infinite-dimensional Lie algebras
KW  - Representation theory
KW  - Mathematical physics
N1  - Includes bibliographical references and index; Algebras -- Examples of Lie algebras -- Lie groups -- Lie algebra basics -- Cartan decomposition -- Semisimple Lie algebras -- Root systems -- PBW and free Lie algebras -- Chevalley bases -- Kac-Moody Lie algebras -- Integrable representations -- Character theory -- Infinite-dimensional Lie algebras -- Virasoro algebra
N2  - This graduate-level textbook presents a modern introduction to the theory of Lie algebras, covering both finite-dimensional and infinite-dimensional structures. Beginning with the algebraic foundations and classical examples of Lie algebras and Lie groups, the book develops the structural theory of semisimple Lie algebras, including Cartan decompositions, root systems, and the Killing-Cartan classification. The author further explores representation theory, Chevalley bases, universal enveloping algebras, and integrable representations. A substantial portion of the text is devoted to infinite-dimensional Lie algebras, including Kac-Moody algebras, affine Lie algebras, loop algebras, and the Virasoro algebra, together with applications to geometry, mathematical physics, and differential equations. Combining rigorous mathematical development with historical context, examples, and exercises, the book serves as a comprehensive resource for graduate students and researchers in algebra, geometry, and theoretical physics
ER  -