Giulietta's changelog

Differential geometry (April-May 2022)

Measure and positive linear form (Kakutani-Riesz representation theorem).
Frobenius theorem

Differential geometry (March 2022)

Kakutani theorem
Immersions are local embeddings.

SU(2) (February 2022)

Put some order in the statements about the Lie group structure of SU(2).
Add some statement about analyticity
Lie group smooth morphisms have constant rank.

Manifolds (January 2021)

Be more precise and systematic about

definition of charts
tangent vectors
integration

Lorentz (December 2019-January 2020)

Adjoint
Boost
Standard decomposition

sl(2,C) (Augustus 2019)

Finite dimensional irreducible representations of the Lie algebra sl(2,C)

Suppress the dependency 'exocorr' (2019 June)

Add \input{exocorr} in e_mazhe.tex. The file exocorr.tex is now essentially a copy of exocorr.sty[1].
Not that dependency anymore.
Update the tutorials COMPILATION_frido.md and COMPILATION_giulietta.md

[1] https://github.com/LaurentClaessens/exocorr

Exponential map and Taylor expansion for Lie groups (2019 May - 2019 June)

Definition of the exponential from the left-invariant vector fields
A Lie group must be analytical
Taylor formula
Proof of exp(A+B+t^2[A,B]/2)=exp(tA)exp(tB)+o(t^2)

SU(2) (2018 December - ...)

The Pauli matrices
Isomorphism SO(3)=SU(2)/Z2.
Continuous paths lifted from SO(3) to SU(2)
Representations of U(1)

Lie subgroup (2019 January)

Prove the rank theorem for maps between manifolds.
Prove that a Lie subgroup is a submanifold.
Separate Lie group/Lie algebra/links in three chapters.

Giulietta (2019 January 1)

Change the name 'mazhe'/'everything' -> 'giulietta'.

Lie algebra of a matrix Lie group (2018 December)

Settle the identification between the tangent vectors on GL(n) as differential operators and the derivative of a path in GL(n) a matrix.

Unitary operators (2018 December)

definition of a unitary operator on a separable Hilbert space
center of SU(n)