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Representations of Solvable Lie Groups
2020International audience; The theory of unitary group representations began with finite groups, and blossomed in the twentieth century both as a natural abstraction of classical harmonic analysis, and as a tool for understanding various physical phenomena.
Arnal, Didier, Currey, Bradley
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The Adjoint Representation of a Lie Group
1993Every group G acts on itself by inner automorphisms: the map associated with an element g is h ↦ ghg −1. If G is a Lie group, the differential of each inner automorphism determines a linear transformation on the tangent space to G at the identity element, because the identity is fixed by any inner automorphism.
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Etale Affine Representations of Lie Groups
1998Let G be a finite-dimensional connected Lie group with Lie algebra g. Denote by E a real vector space and by Aff(E) the group of affine automorphisms $${\text{Aff}}\left( E \right) = \left\{ {\left( {\begin{array}{*{20}{c}} A&b \\ 0&1 \end{array}} \right)|A \in {\text{GL}}\left( E \right),{\text{ }}b \in E} \right\}$$ .
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Representations of solvable Lie groups [PDF]
Functional Analysis and Its Applications, 1977 openaire +1 more source
Group Representations and Lie Algebras
2011Riccardo D'Auria, Mario Trigiante
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Representability of Lie Algebras and Lie Groups by Matrices
The Annals of Mathematics, 1937openaire +2 more sources