7 problems

Let $R$ be a commutative unital ring, let $m,n\geq 1$, and let $E^{m}$ be the $m$-generated Grassmann algebra … For $k\geq 1$, the standard polynomial is … It is a standard identit…

Let $F$ be a field of characteristic different from two, and let $G(n)$ be the Grassmann algebra … A maximal commutative subalgebra is a commutative subalgebra maximal with respect…

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…

Let $n=4k+9$ with $k\geq 2$, and define … where $\mathcal{C}$ is the constructed maximal commutative algebraic system. $K_n$ bound conjecture. Is $K_n<1$ for all $n=4k+9$ with…

Grassmann-envelope conjecture. Any associative $F$-algebra with involution satisfies the same $*$-identities as $E(C)$ for some associative superalgebra…

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…

Self-duality conjecture. For every $f\in {\bf{L}}_{{\mathfrak{B}}_{{L},\mathrm{ev}}}({\mathfrak{B}}_{{L},\mathrm{od}}:{\mathfrak{B}}_{{L}})$, there exists…