I'm interested in dream mathematics (https://ncatlab.org/nlab/show/dream+mathematics) as a foundation of "synthetic measure theory" in a similar vein as synthetic differential geometry, but I'm unclear on its relationship to ordinary mathematics, particularly as expressed through topos theory.
As...
Yes, there are several. Here's a few which I personally care about (described in varying amounts of precision). This is not meant to be an exhaustive list, and reflects my own biases and interests.
I am focusing here on questions which have been open for a long amount of time, rather than questi...
I am interested in explicit formulae for the Casimir elements (or "Casimir operators") of low-dimensional, real, non-Abelian Lie algebras (d=2,3, and possibly 4). I am wondering if there is any reference with a list of, at least some, expressions for such Casimir elements.
Even a few explicit exp...
Let $G$ be a compact Lie group (not necessarily connected) and $\rho:G\to \mathrm{End}(V)$ an irreducible (hence finite-dimensional) unitary representation of $G$. Let $\mathfrak{g}$ be the Lie algebra of $G$, $\mathfrak{U}(\mathfrak{g})$ the universal enveloping algebra, and write also $\rho$ fo...
I am looking for a complete description (if possible with proof) of the
Casimir operators (i.e., generators and relations for the center of the universal enveloping algebra) for the Jacobi Lie algebra over the complex numbers, the semidirect product of the symplectic Lie algebra with a Heisenberg...
Woodin's omega conjecture. See this pdf
Given a general Lie algebra, is there a general procedure to find all its Casimir operator?
