3 problems

Let $G(4k+9)$ be the Grassmann algebra, let $G_0$ denote its even component, and let $M_{\mathcal{C}}$ be the subspace associated with the constructed maximal commutative algebraic…

Converse conjecture. The algebras ${\mathcal B}_{G_1}^T$ and ${\mathcal B}_{G_2}^T$ are isomorphic if and only if the bridge-free matroids of $G_1$ and $G_2$ are isomorphic.

Let $E$ be the Grassmann algebra and let $A_1,A_2\subseteq E$ be maximal-dimensional commutative subalgebras. Uniqueness conjecture. If $n=4k+3$, then $A_1\cong A_2$. This asks whe…