14 problems

Let $\Gamma(n)$ denote the Grassmann algebra with $n$ generators, and let $\mathcal{R}_{a,b}$, $S_{a,b}$, and $T_{a,b}$ be the maps introduced in the paper, with $x_{11}$ and…

Let $\Gamma(n)$ be a Grassmann algebra, and consider the commutative map obtained from the parametric Grassmann Yang–Baxter map by the same restriction procedure used for…

Let $E=\varepsilon_{0}\oplus\varepsilon_{1}$ be an arbitrary $\mathbb{Z}_{2}$-grading on the Grassmann algebra, and let $L$ be its underlying vector space. Homogeneous-generator co…

Let $L$ be the vector space underlying the Grassmann algebra $E$, and let $E=\varepsilon_{0}\oplus\varepsilon_{1}$ be a $\mathbb{Z}_{2}$-grading. A basis of $L$ is called adapted t…

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, and call a commutative subalgebra maximal commutative if it is maximal with respec…

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…

Brandão Jr., Koshlukov, Krasilnikov and Silva's uniqueness conjecture. The limit $T$-subspace in $F\langle X\rangle$ is unique: there are no limit $T$-subspaces in…

Let $C_0,C_1$ be even supernumbers in the Grassmann ring $4\Lambda_{even}4$, and consider the implicit equation … Assume that the relevant elliptic functions can be consistently ge…

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