44 problems

Let $\mathfrak{g}$ be a semisimple Lie algebra with invariant bilinear form $B_{\mathfrak{g}}$, Cartan subalgebra $\mathfrak{h}$, and odd Harish-Chandra projection … Let…

Let $M$ be the underlying vector space, and let $\tau=\triangle^\rho$ and $\rho=\triangle^\rho$ be the coproduct and product data determined by…

Let $V$ be a real inner-product vector space with positive-definite metric $g$. For a finite set of real skew-symmetric endomorphisms $C_1,\ldots,C_r$ satisfying the Clifford relat…

Let $X$ be a space, let $\Gamma_n$ act on $X^n$, and let ${\bf n}=X^n\times{\Bbb C}^n$ be the associated rank-$n$ $\Gamma_n$-vector bundle with its standard quadratic form. Let…

Let an off-shell representation of supersymmetry in any dimension be given, and let a Clifford supermodule be equipped with a filtration or, possibly, a bifiltration. Suppose moreo…

Innerness criterion. The outer automorphism $SO(d-1,1)$ becomes an inner automorphism if and only if

A multicomplex space is a commutative analogue of a Clifford algebra with generators subject to the relevant multicomplex relations. Price's Theorems 46.19 and 46.22 concern formul…

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 $\mathcal{C}$ be a Clifford algebra over a number field. Let $\mathcal{O}_1,\ldots,\mathcal{O}_n$ represent the isomorphism classes of maximal orders, and let…

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…

Inverse-expression conjecture. The inverse of a general multivector of an arbitrary Clifford algebra can always be expressed as a linear combination of a proper number of specially…

K-theoretic Clifford algebra isomorphism conjecture. The map $\gamma$ is an isomorphism.

Let $C\ell_{p,q}$ be a real Clifford algebra, and suppose it is realized as an image of the group algebra $\mathbb{R}[G]$ of a suitable $2$-group $G$. Walley's conjecture. The grou…

Let $Y\subset U_{\overline\Sigma}$ be the complete intersection defined by the equations $f_i=0$, let $\mathcal{S}=[Y/\overline G]$, and let $\mathcal{B}_0$ be the even part of the…

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…

Let $\varDelta_m$ $(m\geqslant 1)$ be the sequence of edge-coloured graphs, each with two edge colours, constructed in the cited work. Colour-swapping automorphism conjecture. For…