H. Cuypers

activity

20142026

most citedCharacterizations of symplectic polar spaces

3 citations · 5 across the 12 of their papers we have counts for

collaborators

13 papers

math.CO2026

On Orthogonal Graphs and their Automorphisms

Hans Cuypers

We provide a characterization of the connected subgraphs of the graphs with vertex set the non-isotropic points in a quadratic space $(V, Q)$ , two points adjacent if and only if the…

quant-ph2026

Dynamical Lie algebras generated by Pauli strings and quadratic spaces over $F_{2}$

Hans Cuypers

Dynamical Lie algebras, i.e. Lie subalgebras of $su (2^{n})$ , generated by Pauli strings have recently been studied intensively. They are also called Pauli Lie algebras or…

math.AC2026

Graphs, Axial Algebras and their Automorphism Groups

Hans Cuypers

We introduce a class of algebras over a field $F$ related to directed graphs in which all edges are labeled by nonzero elements of the field $F$ . If all labels ar…

math.SG2022★ 3 cited

Characterizations of symplectic polar spaces

Ilaria Cardinali, Hans Cuypers, Luca Giuzzi +1

A polar space S is said to be symplectic if it admits an embedding e in a projective geometry PG(V) such that the e-image e(S) of S is defined by an alternating form of V. In this…

math.RA2021★ 1 cited

A geometric characterization of the finitary special linear and unitary Lie algebras

Hans Cuypers, Marc Oostendorp

An extremal element $x$ in a Lie algebra $g$ is an element for which the space $[x, [x, g]]$ is contained in the linear span of $x$ . Long root elements in cla…

math.CO2021

Line graphs of Multi-Graphs and the forbidden graph $E_{6}$

Hans Cuypers

The line graph $Γ$ of a multi-graph $Δ$ is the graph whose vertices are the edges of $Δ$ , where two such edges are adjacent if and only if they meet in a single vertex of $Δ$ . We p…

math.CO2021★ 1 cited

Whitney's Theorem for Line Graphs of Multi-Graphs

Hans Cuypers

Whitney's Theorem states that every graph, different from $K_{3}$ or $K_{1, 3}$ , is uniquely determined by its line graph. A $1$ -line graph of a multi-graph is the graph with as verti…

math.RA2021

Quasi-Clifford algebras, Quadratic forms over $F_{2}$ , and Lie Algebras

Hans Cuypers

Let $Γ = (V, E)$ be a graph, whose vertices $v \in V$ are colored black and white and labeled with invertible elements $λ_{v}$ from a commutative and associ…

math.CO2017

The geometry of hyperbolic lines in polar spaces

Hans Cuypers

In this paper we consider partial linear spaces induced on the point set of a polar space, but with as lines the hyperbolic lines of this polar space. We give some geometric charac…

math.GR2017

On some subgroups of linear groups over $F_{2}$ generated by elements of order $3$

Hans Cuypers

Let $V$ be a vector space over the field of order $2$ . We investigate subgroups of the linear group $G L (V)$ which are generated by a conjugacy class $D$ of elements of order $3$ su…

math.RA2017

A geometric characterization of the symplectic Lie algebra

Hans Cuypers, Yael Fleischmann

A nonzero element $x$ in a Lie algebra $g$ with Lie product $[,]$ is called extremal if $[x, [x, y]]$ is a multiple of $x$ for all $y$ . In this paper we characterize the…

math.RA2017

A geometric characterization of the classical Lie algebras

Hans Cuypers, Yael Fleischmann

A nonzero element x in a Lie algebra g over a field F with Lie product [ , ] is called a extremal element if [x, [x, g]] is contained in Fx. Long root elements in classical Lie alg…

math.RA2014

Recovering the Lie algebra from its extremal geometry

Hans Cuypers, Kieran Roberts, Sergey Shpectorov

An element $x$ of a Lie algebra $L$ over the field $F$ is extremal if $[x, [x, L]] = F x$ . Under minor assumptions, it is known that, for a simple Lie algebra $L$ , the extremal geometry…

On Orthogonal Graphs and their Automorphisms

Dynamical Lie algebras generated by Pauli strings and quadratic spaces over F2​

Graphs, Axial Algebras and their Automorphism Groups

Characterizations of symplectic polar spaces

A geometric characterization of the finitary special linear and unitary Lie algebras

Line graphs of Multi-Graphs and the forbidden graph E6​

Whitney's Theorem for Line Graphs of Multi-Graphs

Quasi-Clifford algebras, Quadratic forms over F2​, and Lie Algebras

The geometry of hyperbolic lines in polar spaces

On some subgroups of linear groups over F2​ generated by elements of order 3

A geometric characterization of the symplectic Lie algebra

A geometric characterization of the classical Lie algebras

Recovering the Lie algebra from its extremal geometry

Dynamical Lie algebras generated by Pauli strings and quadratic spaces over $F_{2}$

Line graphs of Multi-Graphs and the forbidden graph $E_{6}$

Quasi-Clifford algebras, Quadratic forms over $F_{2}$ , and Lie Algebras

On some subgroups of linear groups over $F_{2}$ generated by elements of order $3$