# Index [[Abelian Lie algebras]] [[Adjoint map]] [Ado's Theorem](Ado's%20Theorem) [[Baker-Campbell-Hausdorff formula]] [[Baker-Campbell-Hausdorff lemma]] [[Generalized orthogonal group]] [[Glauber formula]] [[Heisenberg group]] [[Intertwining map of a Lie group representation]] [[Irreducible Lie group representation]] [[Lie algebra homomorphisms]] [[Lie algebra isomorphism]] [[Lie algebra representation]] [[Lie algebra representation]] [[Lie algebras]] [[Lie bracket]] [[Lie group homomorphisms]] [[Lie group isomorphisms]] [[Lie group representations]] [[Lie groups]] [[Lie product formula]] [[Lorentz Group]] [[Matrix Lie group]] [[Non-matrix Lie groups]] [[O(n)]] [[One-parameter groups]] [[One-parameter unitary groups]] [Poisson algebra](Poisson%20algebra) [[Simply connected Lie groups]] [[SL(n;R) and SL(n;C)]] [[SO(3)]] [[SO(n)]] [[SU(2) to SO(3) Lie group homomorphism]] [[SU(2)]] [[SU(n)]] [[U(1)]] [[U(n)]] [Universal cover of a Lie group](Universal%20cover%20of%20a%20Lie%20group.md) --- # Proofs and examples [[Proof of the emergence of Lie algebra homomorphisms from Lie group homomorphisms]] [[Proof of the Glauber formula]] [[Proofs of the Baker-Campbell-Hausdorff lemma]] [[Proofs of the properties of the elements of Matrix Lie Algebras]] [[Proofs of properties of Lie group homomorphisms in relation to Lie algebra homomorphisms]] [[Proof that the commutator is an adjoint map of a Lie Algebra]] [[Proof that the Lie Algebra that corresponds with an Abelian Lie Group is also Abelian]] --- # Bibliography [Hall, B., _Lie Groups Lie Algebras and Representations_, Springer, 2nd edition, 2015.](Hall,%20B.,%20Lie%20Groups%20Lie%20Algebras%20and%20Representations,%20Springer,%202nd%20edition,%202015..md) Hall, Brian. _Quantum Theory for Mathematicians_ %20-%20Quantum%20Theory%20for%20Mathematicians%20(2013,%20Springer-Verlag%20New%20York)%20-%20libgen.lc.pdf) [Schollwöck, U. Homework 1, Quantum Mechanics 1 (German) (2019-2020)](Schollwöck,%20U.%20Homework%201,%20Quantum%20Mechanics%201%20(German)%20(2019-2020).md) [Woit, Peter. _Quantum Theory, Groups and Representations: An Introduction_, Springer, 2017](Woit,%20Peter.%20Quantum%20Theory,%20Groups%20and%20Representations%20An%20Introduction,%20Springer,%202017.md) #MathematicalFoundations/Algebra/AbstractAlgebra/GroupTheory/Lie/LieGroups/Algebras/LieAlgebras #MathematicalFoundations/Algebra/AbstractAlgebra/GroupTheory/Lie/LieGroups #MathematicalFoundations/Algebra/AbstractAlgebra/RepresentationTheory #Bibliography #index