4 problems

Homogeneous realization conjecture. Every $\mathbb{Z}_{2}$-grading of $E$ is $\mathbb{Z}_{2}$-graded isomorphic to some homogeneous $\mathbb{Z}_{2}$-grading of $E$.

Let $K$ be the ground field, let $E$ denote the Grassmann algebra, and let $R$ be a PI-algebra with … where each $R_i$ is one of $K$, $E$, $M_2(K)$, or $E\otimes_K E$, and at least…

The Grassmann-algebraic Pachner-move invariant. The expression

Consider the $2\to4$ Pachner move replacing the 4-simplices $(12345)$ and $(12346)$ by $(12356)$, $(12456)$, $(13456)$, and $(23456)$. Let $\tilde{\mathcal W}_{ijklm}$ denote the c…