Related papers: Semi-invertible extensions and asymptotic homomorp…

For any ring $A$ and a small, preadditive, Hom-finite, and locally bounded category $Q$ that has a Serre functor and satisfies the (strong) retraction property, we show that the category of additive functors from $Q$ to the category of…

In this paper we prove that the homotopy class of non-homothety linear endomorphisms on $\mathbb{T}^2$ with determinant greater than 2 contains a $C^1$ open set of non-uniformly hyperbolic endomorphisms. Furthermore, we prove that the…

The normalized cochain complex of a simplicial set N^*(Y) is endowed with the structure of an E_{infinity} algebra. More specifically, we prove in a previous article that N^*(Y) is an algebra over the Barratt-Eccles operad. According to M.…

An interesting result by T. Kato and A. Pazy says that a contractive semigroup (T(t)) on a uniformly convex space X is holomorphic iff limsup_{t \downarrow 0} ||T(t)-Id|| < 2. We study extensions of this result which are valid on arbitrary…

We study the semigroup extension $\mathscr{I}_\lambda^n(S)$ of a semigroup $S$ by symmetric inverse semigroups of a bounded finite rank. We describe idempotents and regular elements of the semigroups $\mathscr{I}_\lambda^n(S)$ and…

In this paper, we discuss the structure of doubly commuting semigroups of isometries. We record a new proof of Cooper's theorem in the Hilbert module setting. We discuss the Fell topology on the set of equivalence classes of irreducible,…

Let $G$ be a locally compact, Hausdorff, second countable groupoid and $A$ be a separable, $C_0(G^{(0)})$-nuclear, $G$-$C^*$-algebra. We prove the existence of quasi-invariant, completely positive and contractive lifts for equivariant,…

In this paper, we show that every completely semi-$\phi$-map on a submodule of a Hilbert $C^*$-module has a completely semi-$\phi$-map extension on the whole of module. We also investigate the extendability of $\phi$-maps and provide…

In this paper we construct a family of holomorphic functions $\beta_\lambda (s)$ which are solutions to the asymptotic tetration equation. Each $\beta_\lambda$ satisfies the functional relationship ${\displaystyle \beta_\lambda(s+1) =…

In this paper we introduce and investigate the notion of semiseparable functor. One of its first features is that it allows a novel description of separable and naturally full functors in terms of faithful and full functors, respectively.…

We develop the homotopy theory of semisimplicial sets constructively and without reference to point-set topology to obtain a constructive model for $\omega$-groupoids. Most of the development is folklore, but for a few results the author is…

Let $G$ be a connected complex algebraic group and $A$ a connected abelian algebraic group endowed with an algebraic action of $G$ by group automorphisms. In the present note we describe the abelian group $\Ext_{alg}(G,A)$ of algebraic…

Let $k$ be a field, and $H$ a Hopf algebra with bijective antipode. If $H$ is commutative, noetherian, semisimple and cosemisimple, then the category ${}_{H}{\mathcal {YD}}^H$ of Yetter-Drinfeld modules is semisimple. We also prove a…

A stable $\infty$-category is $1$-semiadditive if the norms for all finite group actions are equivalences. In the presence of $1$-semiadditivity, Goodwillie calculus simplifies drastically. We introduce two variants of $1$-semiadditivity…

Let $A$ be a separable amenable $C^*$-algebra and $B$ a non-unital and $\sigma$-unital simple $C^*$-algebra with continuous scale ($B$ need not be stable). We classify, up to unitary equivalence, all essential extensions of the form $0…

Let $(S, \n)$ be a commutative noetherian local ring and $\omega\in\n$ be non-zerodivisor. This paper deals with the behavior of the category $\mon(\omega, \cp)$ consisting of all monomorphisms between finitely generated projective…

This paper develops the homological backbone of the theory of non-commutative $n$-ary $\Gamma$-semirings. Starting from an $n$-ary $\Gamma$-semiring $(T,+,\tilde{\mu})$ and its $\Gamma$-ideals, we work in the slot-sensitive categories of…

Let $C,A$ be countable abelian groups. In this paper we determine the complexity of classifying extensions $C$ by $A$, in the cases when $C$ is torsion-free and $A$ is a $p$-group, a torsion group with bounded primary components, or a free…

We explicitly construct a dynamically incoherent partially hyperbolic endomorphisms of $\mathbb{T}^2$ in the homotopy class of any linear expanding map with integer eigenvalues. These examples exhibit branching of centre curves along…

Given a finite group $G$ and a commutative ring $G$-spectrum $R$, we study the separable commutative algebras in the category of compact $R$-modules. We isolate three conditions on the geometric fixed points of $R$ which ensure that every…