17 problems

Equivalence conjecture. $A$ is zJpd if and only if it is zpd.

Classification conjecture. Every algebra of Jordan type is either a Jordan algebra, a Matsuo algebra, or a factor of a Matsuo algebra.

Let $F$ be a field of characteristic different from $2$. Let $J$ be a Jordan algebra over $F$ generated by idempotents, and let a $\mathcal{J}(\frac{1}{2})$-axial central extension…

Nonexistence conjecture. For $n=6$, one has

Polynomial codimension conjecture. The codimensions of $A^{(2)}_{r,k_1,k_2}$, $A^{(3)}_{k_1,k_2,k_3}$, and $B^{(2)}_{k,\ell_1,\ell_2}$ in…

Let $M$ and $N$ be von Neumann algebras of type II. Write $\mathcal{P}(M)$ and $\mathcal{P}(N)$ for their projection lattices, and let $LS(M)$ and $LS(N)$ denote their algebras of…

Conjecture 3. For every $k\geq 1$,

Conjecture 2. For every $k\geq 1$,

Weak form of Conjecture 1.

Conjecture 1. In ${\cal R}_{an}(GL(D))$,

The weakest dimension conjecture. The sequence $(a_n)_{n\geq 1}$ is the unique solution of

Jordan triple-system conjecture. There is an isomorphism

Let a state space be a convex set whose states admit spectral decompositions, and call it symmetric when any $n$-frame can be transformed into any other $n$-frame by an affine map…

Let $S$ be a finite-dimensional convex compact set that is spectral, meaning that all of its states have orthogonal decompositions with a common spectrum, and suppose that the symm…

Jordan-algebra representation conjecture. If $C$ has a local regret function and a transitive symmetry group, then $C$ can be represented as the positive elements of a Jordan algeb…

Let $(X,(U_x)_{x\in X})$ be a proper Moufang set, meaning that its little projective group is not sharply $2$-transitive, and suppose that each root group $U_x$ is abelian. A quadr…

Let $\mathcal T$ be a real finite-dimensional representation of $SO(3)$ of the form … where $W_{0}$, $W_{1}$, and $W_{2}$ are respectively the weight $0$, natural, and symmetric tr…