21 problems

Let $C$ be a doubly even binary code of length $n$, and let $\Lambda_C$ be the inverse image of $C$ under the natural map … Let $\mathbb{Z}[\frac{1}{2}\Lambda_C]$ denote the ring g…

Let $\mathbb{C}_n$ be the Clifford algebra with generators $i_1,\ldots,i_{n-1}$, and let $\mathbb{Z}[i_1,\ldots,i_{n-1}]$ be the indicated Clifford order. A maximal order is closed…

Let $\mathcal{O}$ be an order in the relevant Clifford algebra, and suppose that it is Clifford-Euclidean, meaning that it admits the Clifford-Euclidean division property used to c…

Let $\mathcal{O}_{5,!}$ be the oddball maximal order, and let $\operatorname{Vec}(\mathcal{O}_{5,!})$ denote its vector part. A right ideal generated by…

Let $C\subset \mathbb{F}_2^n$ be a maximal doubly even binary code, and let $I=(i_0,i_1,\ldots,i_{n-1})$. Consider the Clifford algebra $\mathbb{C}_n$ and the rational Clifford alg…

Let $X$ be the base of the Calabi–Yau double cover $Y$, let $Cl_{0}$ be the even part of the sheaf of Clifford algebras obtained from the quadratic GLSM superpotential, and write…

Let $A$ be a commutative ring with unit in which $2\neq0$, let $(N,Q)$ be a quadratic module over $A$, and set $\mathcal{C}:=\mathcal{C}(N,Q)$. Let $e$ be the idempotent used to fo…

Let $\mathcal{S}=[Y/\overline G]$ be the quotient stack associated with a general Clifford mirror, and let $\mathcal{B}_0$ denote its even Clifford-algebra sheaf. Assume the centra…

Let $(\mathcal{S},\mathcal{B}_0)$ be the Clifford-limit object defined using the central even Clifford algebra sheaf, and let $D_B(K,c,\Sigma)$ denote the category associated with…

Let the Clifford double mirror of Definition be the Clifford construction associated with the two quartics $\mathbb{Q}_+$ and $\mathbb{Q}_-$ in $\mathbb{C}\mathbb{P}^3$. The corres…

Let $m\geqslant 0$ and let $\mathbb{R}_{m,m}$ be the real representation of the Clifford algebra. A transversal graph is an induced complete subgraph on $2^m$ vertices whose edges…

Let $m\geqslant 0$ and let $\mathbb{R}_{m,m}$ be the real representation of the Clifford algebra. A transversal graph is an induced complete subgraph on $2^m$ vertices, and its edg…

Let $m\geqslant 0$. Consider the $4^m$ canonical basis matrices of the real representation of the Clifford algebra $\mathbb{R}_{m,m}$; a pair has disjoint support when the supports…

Sойбельman's conjecture. The full COHA for the quiver $A_1$ is isomorphic to $Cl_c$, with mixed generators satisfying

Rank monotonicity conjecture. The obtained representation of $C_f$ has rank no less than the rank of the initial representation of $C_g$.

Let $Q$ be a quiver with one vertex and $m$ arrows. For even $m$, let $Cl_c$ denote the infinite Clifford algebra with generators $\xi_n^{+}$ and $\xi_n^{-}$ for…

Cohomological dimension conjecture. For $d535a,d535b\in\mathcal{E}(\mathcal{CL})$,

Let $X$ be a smooth projective curve and let $E$ be an irreducible $\operatorname{SL}_2$-local system on $X$ such that, for every $d\ts 0$ and every covering $\phi:Y\to X$ in…

Read-inspired isomorphism conjecture. There is a superalgebra isomorphism

Let $\mathfrak{g}=\mathfrak{n}_+\oplus\mathfrak{h}\oplus\mathfrak{n}_-$ be a Lie algebra with triangular decomposition, let $\operatorname{Cl}(\mathfrak{g})$ be its Clifford algebr…

Let $Q$ be a conic bundle and let $\operatorname{Cl}_0(Q)$ be its even Clifford algebra. Consider orders Morita equivalent to $\operatorname{Cl}_0(Q)$ and having the same rank and…