Course Details
Subject {L-T-P / C} : MA5118 : Lie Algebra { 3-0-0 / 3}
Subject Nature : Theory
Coordinator : Prof. Kishor Chandra Pati
Syllabus
Introduction to Lie group,Lie algebra,Relation between the two.Definition of Lie algebra,Classification of some low dimensional Lie algebras. Concept of Lie group through symmetry and transformations, Bilinear forms and construction of classical lie groups and classical lie algebras,
Lie sub algebra, Ideals, Solvable and Nilpotent lie algebras, radical, Levi decomposition theorem, Simple and semisimple Liealgebras
Homomorphism, Isomorphism of Lie algebras, Introduction to representation theory of Lie algebras, Highest weight represention of lie algebras,
Jordan Chevelley decomposition of lie algebras,Concept of Toral subalgebras, Roots and Root spaces.Properties of Roots, Chevelley basis, Cartan matrix,Dynkin diagrams, Determination of Roots and Root diagrams of classical lie algebras, Introduction to Kac Moody algebras
Course Objectives
- After learning this course , one will learn basics of lie algebra and understand the application part of it in engineering and sciences.
Course Outcomes
Elementary knowledge on Lie algebras
Essential Reading
- J E Humphreys, Introduction to Lie algebras and Representation Theory, Springer-Verlag
- Alexander Kirillov, JR., An introduction to Lie Groups and Lie algebras, CUP
Supplementary Reading
- J E Humpherys, Introduction to lie algebras and representation theory, Springer-Verlag
- Alexander Kirillov,JR., Introduction to Lie groups and Lie algebras, CUP