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A fundamental result of Banyaga states that the Hamiltonian diffeomorphism group of a closed symplectic manifold is perfect. We refine this result by proving that, locally in the $C^\infty$ topology, the number of commutators needed to…
We describe maximal commutative unipotent subgroups of the automorphism group $\mathrm{Aut}(X)$ of an irreducible affine variety $X$. Further we show that a group isomorphism $\mathrm{Aut}(X) \to \mathrm{Aut}(Y)$ maps unipotent elements to…
We start developing a formalism which allows to construct supersymmetric theories systematically across space-time signatures. Our construction uses a complex form of the supersymmetry algebra, which is obtained by doubling the spinor…
We provide a method, based on Nikulin's lattice gluing techniques, which identifies the symplectic automorphisms of Kummer surfaces as permutation groups on 24 elements preserving the Golay code. In other words, we explicitly realise these…
The $2$-adic ring $C^*$-algebra $\mathcal{Q}_2$ naturally contains a copy of the Cuntz algebra $\mathcal{O}_2$ and, a fortiori, also of its diagonal subalgebra $\mathcal{D}_2$ with Cantor spectrum. This paper is aimed at studying the group…
We prove that the topological full group $[[X]]$ of a two-sided full shift $X = \Sigma^{\mathbb{Z}}$ contains every right-angled Artin group (also called a graph group). More generally, we show that the family of subgroups with "linear…
The cohomology of the pure string motion group PSigma_n admits a natural action by the hyperoctahedral group W_n. Church and Farb conjectured that for each k > 0, the sequence of degree k rational cohomology groups of PSigma_n is uniformly…
We study locally closed transformation monoids which contain the automorphism group of the random graph. We show that such a transformation monoid is locally generated by the permutations in the monoid, or contains a constant operation, or…
Answering a question of Conway and Guy in a 1968 paper, L\'angi in 2021 proved the existence of a monostable polyhedron with $n$-fold rotational symmetry for any $n \geq 3$, and arbitrarily close to a Euclidean ball. In this paper we…
Let $\Bbbk$ be a perfect field with algebraic closure $\overline{\Bbbk}$. If $H$ is a subgroup of plane automorphisms over $\Bbbk$ and $p\in\overline{\Bbbk}^2$ is a point, we describe the subgroup consisting of plane automorphisms which…
We study cohomogeneity one Riemannian manifolds and we establish some simple criterium to test when a singular orbit is totally geodesic. As an application, we classify compact, positively curved Riemannian manifolds which are acted on…
A monoid is said to be special if it admits a presentation in which all defining relations are of the form $w = 1$. Groups are familiar examples of special monoids. This article studies the geometric and structural properties of the Cayley…
We study the representation of a finite group acting on the cohomology of a non-degenerate, invariant hypersurface of a projective toric variety. We deduce an explicit description of the representation when the toric variety has at worst…
Let $\mathcal M$ be a compact complex supermanifold. We prove that the set $\mathrm{Aut}_{\bar 0}(\mathcal M)$ of automorphisms of $\mathcal M$ can be endowed with the structure of a complex Lie group acting holomorphically on $\mathcal M$,…
We show that the linear symplectic and anti-symplectic transformations form the maximal covariance group for both the Wigner transform and Weyl operators. The proof is based on a new result from symplectic geometry which characterizes…
The paper presents the complete classification of Automorphic Lie Algebras based on $\mathfrak{sl}_n (\mathbb{C})$, where the symmetry group $G$ is finite and the orbit is any of the exceptional $G$-orbits in $\overline{\mathbb{C}}$. A key…
We employ the intertwining operator technique to synthesize a supersymmetric (SUSY) array of arbitrary size $N$. The synthesized SUSY system is equivalent to a spin-$(N-1)/2$ under an effective magnetic field. By considering an additional…
Among the simplest invariants of the sporadic finite simple groups are their outer automorphism groups. For 12 of the 26 possible isomorphism types of a sporadic simple group G, the outer automorphism group Out(G) has order 2, and in the…
String theory, specifically type-II superstring theory, can be formulated in any ten-dimensional signature. To facilitate the study of supergravity and superstring theories in this setting, we present a uniform construction of supersymmetry…
We show that the topological rank of an orbit full group generated by an ergodic, probability measure-preserving free action of a non-discrete unimodular locally compact Polish group is two. For this, we use the existence of a cross section…