Abstract
Symmetry considerations are nowadays an important tool in the mathematical description of most of the theories of modern physics. We present here linear algebraic and Lie groups via their functor of points, and use algebras with involutions to describe classical groups over non-algebraically closed fields. We then discuss Clifford algebras and spinors, and give an introduction to the general structure theory of linear algebraic groups and of their representations. This chapter mostly contains very classical results, and is included for later reference in the description of physical examples.
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Paugam, F. (2014). Linear Groups. In: Towards the Mathematics of Quantum Field Theory. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, vol 59. Springer, Cham. https://doi.org/10.1007/978-3-319-04564-1_5
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DOI: https://doi.org/10.1007/978-3-319-04564-1_5
Publisher Name: Springer, Cham
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