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...

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 $|q|=1$.

A locally compact group G is discrete if and only the Fourier algebra A(G) has a non-zero (weakly) multiplier. We partially extend this result to setting of ultraspherical hypergroups. Let H be an hypergroup let A(H) denote corresponding algebra. will give several characterizations discreteness in terms algebraic properties A(H). also study Arens regularity closed ideals