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Graduate Algebra and Representation Theory Seminar

Matrix Lie groups and their Lie algebras

Jason Saied - Rutgers University

Location:  GSL - Hill 701
Date & time: Monday, 09 September 2019 at 3:10PM - 4:10PM

Abstract: In this introductory talk, we will discuss Lie groups, groups with smooth manifold structures that make multiplication and inversion into smooth maps. To avoid the analytic complications of the general case, we will focus on matrix Lie groups. We will construct the Lie algebra of a matrix Lie group and prove some results allowing us to reduce questions about Lie groups (more complicated, analytic objects) to questions about their Lie algebras (finite dimensional vector spaces with an extra operation). I will only assume basic knowledge of groups, vector spaces, and undergraduate calculus.