1
vote
1answer
70 views

A Non-homogeneous, Linear (Matrix) System of ODEs: What's Known About it? [closed]

Consider the following system of ODEs $$ Y^{'}(t) = - \left[ A Y(t) + Y(t) A \right] + B(t) , $$ where $Y(t)$,$A$,$B(t)$ are all matrices, with the properties $A=A^T$, $Y=Y^T$. $Y(t)$ is the matrix ...
2
votes
1answer
137 views

Parameter dependent differential equation in a Lie group

It is well-known that a linear differential equation in a finite-dimensional vector space depends continuously on some external parameters (for details see below). I search for an explicit reference ...
4
votes
0answers
195 views

A possible refinement of a theorem of Malliavin

Due to a theorem of Malliavin (an improvement of an erlier theorem of Dixmier and Malliavin, see here) we know that every compactly supported smooth function $f$ on $\mathbb R^n$ can be written as a ...
2
votes
3answers
258 views

Non continous representations of $SL_2(\mathbf{R})$

Q: How does one construct a non continuous representation $\rho:SL_2(\mathbf{R})\rightarrow G$ for some connected (finite dimensional) Lie group $G$?
10
votes
1answer
385 views

Lie $2$-groups and differential equations

I was reading the abstract of a recent preprint (Division Algebras and Supersymmetry III by Juhn Huerta), and I wondered if something much simpler than what he was talking about had been worked on: ...
22
votes
1answer
1k views

Monotone functions are differentiable a.e. and Hilbert's Fifth Problem: what's the connection?

In Andrew Gleason's interview for More Mathematical People, there is the following exchange concerning Gleason's work on Hilbert's fifth problem on whether every locally Euclidean topological group is ...
4
votes
2answers
469 views

Abelianization of Lie groups

If G is a group, its abelianization is the abelian group A and the map G → A such that any map G → B with B abelian factors through A. Abelianization is a functor, and in general a very ...