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Thales Fernando Vilamaior Paiva

Publications and source records attributed to Thales Fernando Vilamaior Paiva.

4 recordsLinked to original sources
arXiv2026

Pasting and stability in convergence spaces

We prove a pasting lemma for locally finite closed covers of convergence spaces with limit codomains. We also show how the validity of such lemmas characterizes limit spaces.

math.AT↗
arXiv2026

Just-Infinite Loops and Loop Algebras

Let $F$ be a field and let $L$ be a loop. We call $L$ just-infinite if it is infinite and every nontrivial normal subloop has finite index, and we call the possibly nonassociative loop algebra $F[L]$ just-infinite if it is infinite-dimensional and every nonzero two-sided ideal has finite codimension. We first prove that just-infiniteness of $F[L]$ always implies just-infiniteness of $L$. Next, using the Chein construction, we show for every infinite group $G$ that $M(G,2)$ is just-infinite if and only if $G$ is just-infinite, and that $F[M(G,2)]$ is just-infinite if and only if $F[G]$ is just-infinite. We extend the algebraic equivalence to the generalized Moufang doubles $M(G,*,g_0)$ whenever $G$ is infinite and nonabelian. Finally, we construct a single locally finite, residually finite, nonassociative Moufang loop $L$ for which $F[L]$ is residually finite-dimensional, locally finite-dimensional, and just-infinite over every field, and we explain why infinite nonassociative RA loops cannot be just-infinite.

math.RA↗
arXiv2026

A Cohomological Obstruction to the Existence of $ϕ$-Equivariant Maps

Let $ϕ: G\to H$ be a continuous homomorphism between compact Lie groups, let $X$ be a $G$-space, and let $Y$ be an $H$-space. We formulate a filtered change-of-groups obstruction to the existence of a $ϕ$-equivariant map $X\to Y$. We apply them to the inclusion of a finite cyclic group into the circle and to homomorphisms between tori acting coordinatewise on products of odd-dimensional spheres.

math.AT↗