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Introduction to Lie groups and algebras - 1

Presented by: 
Elizabeth Mansfield
Monday 8th July 2019 - 14:00 to 15:00
INI Seminar Room 1
In this series of three lectures, I will give a gentle introduction to Lie groups and their associated Lie algebras, concentrating on the major examples of importance in applications. I will next discuss Lie group actions, their invariants, their associated infinitesimal vector fields, and a little on moving frames. The final topic will be Noether’s Theorem, which yields conservations laws for variational problems which are invariant under a Lie group action. Time permitting, I will show a little of the finite difference and finite element versions of Noether’s Theorem.

In this first talk, I will consider some of the simplest and most useful Lie groups. I will show how to derive their Lie algebras, and will further discuss the Adjoint action of the group on its Lie algebra, the Lie bracket on the algebra, and the exponential map.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons