This is a short comment on “The impacts of land plant evolution Earth's climate and oxygenation state – An interdisciplinary review” by Tais W. Dahl Susanne K.M. Arens, Chem. Geol. 547 (2020) Article 119665. We discuss what the sedimentary-stratigraphic record (SSR) can reveal about influence ancient plants erosion, demonstrate that intensive properties SSR are supportive hypotheses vegetation ...

Let L be a completely valued nonarchimedean field and g a finite dimensional Lie algebra over L. We show that its hyperenveloping algebra F(g) agrees with its Arens-Michael envelope and, furthermore, is a stably flat completion of its universal enveloping algebra. As an application, we prove that the Taylor relative cohomology for the locally convex algebra F(g) is naturally isomorphic to the L...

We describe the generic change of the partial multiplicities at a given eigenvalue λ0 of a regular matrix pencil A0 + λA1 under perturbations with low normal rank. More precisely, if the pencil A0 + λA1 has exactly g nonzero partial multiplicities at λ0, then for most perturbations B0 + λB1 with normal rank r < g the perturbed pencil A0 + B0 + λ(A1 + B1) has exactly g − r nonzero partial multip...

A Banach lattice algebra is a Banach lattice, an associative algebra with a sub-multiplicative norm and the product of positive elements should be positive. In this note we study the Arens regularity and cohomological properties of Banach lattice algebras.

let $a$ be a $c^*$-algebra and $e$ be a left hilbert $a$-module. in this paper we define a product on $e$ that making it into a banach algebra and show that under the certain conditions $e$  is arens regular. we also study the relationship between derivations of $a$ and $e$.

It was shown in papers of Dosi and a recent article the author that there is sheaf Frechet-Arens-Michael algebras (locally solvable complex case polynomial growth real) on character space nilpotent Lie algebra. For algebra group affine transformations line (the simplest non-nilpotent algebra) we construct analogous sheaves non-commutative smooth holomorphic functions special set representations.

The Arens-Michael functor in noncommutative geometry is an analogue of the analytification algebraic geometry: out ring “algebraic functions” on a affine scheme, it constructs “holomorphic when viewed as complex analytic space. In this paper, we explicitly compute envelopes Jordan plane and quantum enveloping algebra $U\_q(\mathfrak{sl}(2))$ $\mathfrak{sl}(2)$ for $|q|=1$.