arXiv subjects

Felipe I. Flores

Publications and source records attributed to Felipe I. Flores.

9 recordsLinked to original sources

arXiv2026

PHP decompositions and primitivity of group rings for linear groups

We show that every countable group $G$ that has Ozawa's property $\rm PHP$ and contains a non-abelian free subgroup has the following property: the group ring $KG$ is primitive for any field $K$. As a consequence, we deduce that all non-trivial countable linear groups with trivial amenable radical have this property. Along the way, we prove that the class of groups with $\rm PHP$ enjoys some permanence properties that are of independent interest.

math.RA↗

arXiv2026

Mixed-identity-freeness and primitivity of group rings

We show that every countable group $G$ that is mixed-identity-free (MIF) and contains a non-abelian free subgroup has the following property: the group ring $KG$ is primitive for any field $K$. We also present a purely dynamical criterion that implies this result. Our criterion recovers several of the existing results on primitivity, including those involving acylindrically hyperbolic groups. Furthermore, our criterion also applies (positively) to a plethora of new examples, such as Thompson-like groups, commensurator groups of hyperbolic groups, some Kac-Moody groups, and many more.

math.RA↗

arXiv2026

On the continuity of derivations over locally regular Banach algebras

We study the problem of continuity of derivations over Banach algebras. More specifically, we consider a class of Banach algebras that contain a dense '$C^*$-like' subalgebra. We discuss applications to $L^p$-crossed products and symmetrized $L^p$-crossed products. As an example, our results imply that every derivation over the $L^p$-crossed product $F^p(G,X,α)$ is continuous, provided that $G$ is infinite, finitely generated, has polynomial growth, and acts freely on the compact Hausdorff space $X$.

math.FA↗

arXiv2026

On the topological ranks of Banach $^*$-algebras associated with groups of subexponential growth

Let $G$ be a group of subexponential growth and $\mathscr C\overset{q}{\to}G$ a Fell bundle. We show that any Banach $^*$-algebra that sits between the associated $\ell^1$-algebra $\ell^1( G\,\vert\,\mathscr C)$ and its $C^*$-envelope has the same topological stable rank and real rank as $\ell^1( G\,\vert\,\mathscr C)$. We apply this result to compute the topological stable rank and real rank of various classes of symmetrized twisted $L^p$-crossed products and show that some twisted $L^p$-crossed products have topological stable rank 1. Our results are new even in the case of (untwisted) group algebras.

math.OA↗

arXiv2025

A note on finite-dimensional quotients and the problem of automatic continuity for twisted convolution algebras

In this note, we will show that the twisted convolution algebra $L^1_{α,ω}({\sf G},\mathfrak A)$ associated to a twisted action of a locally compact group ${\sf G}$ on a $C^*$-algebra $\mathfrak A$ has the following property: Every quotient by a closed two-sided ideal of finite codimension produces a semisimple algebra. Afterward, we use this property, together with results by H. Dales and G. Willis, to extend previous results by the author and to produce large classes of examples of algebras with automatic continuity properties.

math.FA↗

arXiv2025

Harmonic analysis and automatic continuity in the context of generalized differential subalgebras

For appropriate parameters $k,p,q$, we introduce and systematically study the class of $(k,p,q)$-differential subalgebras. This is a vast class of Banach $^*$-algebras defined by their relation with their $C^*$-envelopes. Some examples are given by normable two-sided $^*$-ideals, domains of closed $^*$-derivations, full Hilbert algebras, and some weighted convolution algebras of various kinds. We prove that this class of algebras possesses various interesting properties, such as closedness under a functional calculus based on smooth functions, $^*$-regularity, Wiener's property $(W)$, and properties of automatic continuity.

math.FA↗

arXiv2025

Polynomial growth and functional calculus in algebras of integrable cross-sections

Let ${\sf G}$ be a locally compact group with polynomial growth of order $d$, a polynomial weight $ν$ on ${\sf G}$ and a Fell bundle $\mathscr C\overset{q}{\to}{\sf G}$. We study the Banach $^*$-algebras $L^1({\sf G}\,\vert\,\mathscr C)$ and $L^{1,ν}({\sf G}\,\vert\,\mathscr C)$, consisting of integrable cross-sections with respect to ${\rm d} x$ and $ν(x){\rm d} x$, respectively. By exploring new relations between the $L^p$-norms and the norm of the Hilbert $C^*$-module $L^2_{\rm e}({\sf G}\,\vert\,\mathscr C)$, we are able to show that the growth of the self-adjoint, compactly supported, continuous cross-sections is polynomial. More precisely, they satisfy $$\|{e^{itΦ}}\|=O(|t|^n),\quad\text{ as }|t|\to\infty,$$ for values of $n$ that only depend on $d$ and the weight $ν$. We use this fact to develop a smooth functional calculus for such elements. We also give some sufficient conditions for these algebras to be symmetric. As consequences, we show that these algebras are locally regular, $^*$-regular and have the Wiener property (when symmetric), among other results. Our results are already new for convolution algebras associated with $C^*$-dynamical systems.

math.FA↗

arXiv2025

Twisted convolution algebras with coefficients in a differential subalgebra

Let $({\sf G},α, ω,\mathfrak B)$ be a measurable twisted action of the locally compact group ${\sf G}$ on a Banach $^*$-algebra $\mathfrak B$ and $\mathfrak A$ a differential Banach $^*$-subalgebra of $\mathfrak B$, which is stable under said action. We observe that $L^1_{α,ω}({\sf G},\mathfrak A)$ is a differential subalgebra of $L^1_{α,ω}({\sf G},\mathfrak B)$. We use this fact to provide new examples of groups with symmetric Banach $^*$-algebras. In particular, we prove that discrete rigidly symmetric extensions of compact groups are symmetric or that semidirect products ${\sf K}\rtimes{\sf H}$, with ${\sf H}$ symmetric and ${\sf K}$ compact, are symmetric.

math.OA↗

arXiv2024

On the continuity of intertwining operators over generalized convolution algebras

Let ${\sf G}$ be a locally compact group, $\mathscr C\overset{q}{\to}{\sf G}$ a Fell bundle and $\mathfrak B=L^1({\sf G}\,\vert\,\mathscr C)$ the algebra of integrable cross-sections associated to the bundle. We give conditions that guarantee the automatic continuity of an intertwining operator $θ:\mathcal X_1\to\mathcal X_2$, where $\mathcal X_1$ is a Banach $\mathfrak B$-bimodule and $\mathcal X_2$ is a weak Banach $\mathfrak B$-bimodule, in terms of the continuity ideal of $θ$. We provide examples of algebras where this conditions are met, both in the case of derivations and algebra morphisms. In particular, we show that, if ${\sf G}$ is infinite, finitely-generated, has polynomial growth and $α$ is a free (partial) action of ${\sf G}$ on the compact space $X$, then every homomorphism of $\ell^1_α({\sf G},C(X))$ into a Banach algebra is automatically continuous.

math.FA↗