Introduction to Lie Algebras

Finite and Infinite Dimension
Lie algebras blend beauty and power, merging finite and infinite-dimensional theory with rich modern insights. The text navigates semisimple algebra classification, introduces Chevalley bases, and unfolds Kac-Moody and Virasoro algebras, linking structures with physics, history, and ongoing mathematical exploration.
Being both a beautiful theory and a valuable tool, Lie algebras form a very important area of mathematics. This modern introduction targets entry-level graduate students. It might also be of interest to those wanting to refresh their knowledge of the area and be introduced to newer material. Infinite-dimensional algebras are treated extensively along with the finite-dimensional ones. After some motivation, the text gives a detailed and concise treatment of the Killing-Cartan classification of finite-dimensional semisimple algebras over algebraically closed fields of characteristic 0. Important constructions such as Chevalley bases follow. The second half of the book serves as a broad introduction to algebras of arbitrary dimension, including Kac-Moody (KM), loop, and affine KM algebras. Finite-dimensional semisimple algebras are viewed as KM algebras of finite dimension, their representation and character theory developed in terms of integrable representations. The text also covers triangular decomposition (after Moody and Pianzola) and the BGG category $\mathcal{O}$. A lengthy chapter discusses the Virasoro algebra and its representations. Several applications to physics are touched on via differential equations, Lie groups, superalgebras, and vertex operator algebras. Each chapter concludes with a problem section and a section on context and history. There is an extensive bibliography, and appendices present some algebraic results used in the book.

UK Delivery:

• Free delivery on all orders of £10 or more.
• £1.49 delivery fee on orders below £10.
• UK orders are shipped via Royal Mail 2nd Class.

International Delivery:

• Flat rate delivery charges vary by country.

Dispatch and Delivery Times:

• All orders are shipped from our warehouse in Northampton, UK within 48 hours of receipt during working hours.
• UK mainland orders typically arrive within 3-5 working days via Royal Mail 2nd Class.
• International estimated delivery times:
• Europe & Channel Islands: 7 to 10 working days
• USA: 7 to 15 working days
• Rest of the World: 9 to 21 working days

View our full delivery infomation here.