Revista de la
Unión Matemática Argentina

Current issue

Articles are published here before the issue is completed.

Vol. 68, no. 2 (2025)

On the second $\mathfrak{osp}(1|2)$-relative cohomology of the Lie superalgebra of contact vector fields on $\mathcal{C}^{1|1}$. Abderraouf Ghallabi, Nizar Ben Fraj, and Salem Faidi
Let $\mathcal{K}(1)$ be the Lie superalgebra of contact vector fields on the $(1,1)$-dimensional complex superspace; it contains the Möbius superalgebra $\mathfrak{osp}(1|2)$. We classify $\mathfrak{osp}(1|2)$-invariant superanti-symmetric binary differential operators from $\mathcal{K}(1)\wedge\mathcal{K}(1)$ to $\mathfrak{D}_{\lambda,\mu}$ vanishing on $\mathfrak{osp}(1|2)$, where $\mathfrak{D}_{\lambda,\mu}$ is the superspace of linear differential operators acting on the superspaces of weighted densities. This result allows us to compute the second differential $\mathfrak{osp}(1|2)$-relative cohomology of $\mathcal{K}(1)$ with coefficients in $\mathfrak{D}_{\lambda,\mu}$.
349–367
Clones from comonoids. Ulrich Krähmer and Myriam Mahaman
We revisit the fact that the cocommutative comonoids in a symmetric monoidal category form the best possible approximation by a cartesian category, now considering the case where the original category is only braided monoidal. This leads to the question of when the endomorphism operad of a comonoid is a clone (a Lawvere theory). By giving an explicit example, we prove that this does not imply that the comonoid is cocommutative.
369–394
Frobenius property for fusion categories of dimension 120. Li Dai
We prove that fusion categories of Frobenius–Perron dimensions 120 are of Frobenius type. Combining this with known results in the literature, we get that all weakly integral fusion categories of Frobenius–Perron dimension less than 126 are of Frobenius type.
395–403
Linear functionals and $\Delta$-coherent pairs of the second kind. Diego Dominici and Francisco Marcellán
We classify all the $\Delta$-coherent pairs of measures of the second kind on the real line. We obtain five cases, corresponding to all the families of discrete semiclassical orthogonal polynomials of class $s\leq1$.
405–422
Finite groups in which some maximal subgroups are MNP-groups. Pengfei Guo and Huaguo Shi
A finite group $G$ is called an MNP-group if all maximal subgroups of the Sylow subgroups of $G$ are normal in $G$. The aim of this paper is to give a necessary and sufficient condition for a group to be an MNP-group, characterize the structure of finite groups whose maximal subgroups (respectively, maximal subgroups of even order) are all MNP-groups, and determine finite non-abelian simple groups whose second maximal subgroups (respectively, maximal subgroups of even order) are all MNP-groups.
423–435