A review on classification of semisimple Lie algebra

Labroo, Rithik (2023) A review on classification of semisimple Lie algebra. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS dissertation of Rithik Labroo (18MS107)) Thesis_18MS107.pdf - Submitted Version Restricted to Repository staff only Download (1MB)

Abstract

This thesis presents a comprehensive study on Lie algebras, focusing on the classification of root systems and Serre’s theorem. The Lie algebra, a fundamental concept in algebraic structures, provides a powerful framework for investigating the algebraic properties of symmetry and transformation. The main objective of this project is to delve into the classification theory of root systems, which play a crucial role in understanding the structure and representation theory of Lie algebras. The thesis begins by introducing the foundational concepts of Lie algebras, including their definitions, and properties. Building upon this foundation, an indepth exploration of root systems is undertaken, elucidating their significance in characterizing the structure of Lie algebras. Various classifications of root systems are investigated, including those associated with classical and exceptional Lie algebras. Furthermore, the thesis delves into Serre’s theorem, a seminal result that establishes a deep connection between root systems and the structure of semisimple Lie algebras. Serre’s theorem provides a powerful tool for analyzing the representation theory and dynamics of Lie algebras. By delving into the classification of root systems and comprehensively examining Serre’s theorem, this thesis aims to understand of Lie algebras and their associated structures.

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