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Description
Lie groups are continuous groups of symmetries, like the group of rotations of n-dimensional space or the group of invertible n-by-n matrices. In studying such groups we can use tools from calculus to linearise our problems, which leads us to the notion of a Lie algebra: a vector space with an antisymmetric product associated to any Lie group, which remembers everything about its algebraic structure. For example, the Lie algebra associated with the group of rotations of 3-space is just 3-dimensional Euclidean space with (twice) the vector cross product.
This course divides in two halves. In the first half we introduce the notion of a Lie algebra and the relationship between a Lie group and its Lie algebra. This will involve some ideas from geometry (manifolds and tangent spaces) which will serve you well in later courses. In the second half we study representations of Lie groups and Lie algebras, paying attention to the groups SU(2) and SU(3). This will be much more algebraic.
Module deliveries for 2024/25 academic year
Last updated
This module description was last updated on 8th April 2024.
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