Related papers: Expansivity of algebraic semigroup actions

We prove that the Flat Cover Conjecture holds for the category of (right) acts over any right-reversible monoid $S$, provided that the flat $S$-acts are closed under stable Rees extensions. The argument shows that the class…

We show that a continuous action of a quantum semigroup $\mathcal{S}$ on a finite quantum space (finite dimensional $\mathrm{C}^*$-algebra) preserving a faithful state comes from a continuous action of the quantum Bohr compactification…

We establish a one-to-one correspondence between rational multiplicative group actions on an algebraic variety $X$ and derivations $\partial\colon K_X\to K_X$ of the field of fractions $K_X$ of $X$ satisfying that there exists a generating…

We study the connection between amenability, F{\o}lner conditions and the geometry of finitely generated semigroups. Using results of Klawe, we show that within an extremely broad class of semigroups (encompassing all groups, left…

An involution on a semigroup S (or any algebra with an underlying associative binary operation) is a function f:S->S that satisfies f(xy)=f(y)f(x) and f(f(x))=x for all x,y in S. The set I(S) of all such involutions on S generates a…

A semigroup $S$ is said to be right pseudo-finite if the universal right congruence can be generated by a finite set $U\subseteq S\times S$, and there is a bound on the length of derivations for an arbitrary pair $(s,t)\in S\times S$ as a…

We initiate the study of the Stone-\v{C}ech transformation groupoid $\mathcal{G} = \mathcal{S}\ltimes\beta\mathcal{S}$ of an inverse semigroup $\mathcal{S}$. We prove that the properties of being Hausdorff, principal, and effective are all…

Given a partial action of a topological group $G$ on a space $X$, we determine properties $\mathcal P$ which can be extended from $X$ to its globalization. We treat the cases when $\mathcal P$ is any of the following: Hausdorff, regular,…

For an inverse semigroup S with the set of idempotents E and a minimal idempotent, we find necessary and sufficient conditions for the Fourier algebra A(S) to be module amenable, module character amenable, module (operator) biflat, or…

We give bordism-finiteness results for manifolds with semi-simple group action. Consider the class of oriented manifolds which admit a circle action with isolated fixed points such that the action extends to an $S^3$-action with fixed…

Consider an algebraic semigroup $S$ and its closed subscheme of idempotents, $E(S)$. When $S$ is commutative, we show that $E(S)$ is finite and reduced; if in addition $S$ is irreducible, then $E(S)$ is contained in a smallest closed…

Motivated by Popa's seminal work \cite{Po04}, in this paper, we provide a fairly large class of examples of group actions $\Gamma \curvearrowright X$ satisfying the extended Neshveyev-St{\o}rmer rigidity phenomenon \cite{NS03}: whenever…

We show that every group $H$ of at most exponential growth with respect to some left invariant metric admits a bi-Lipschitz embedding into a finitely generated group $G$ such that $G$ is amenable (respectively, solvable, satisfies a…

Loday's dendriform algebras and its siblings pre-Lie and zinbiel have received attention over the past two decades. In recent literature, there has been interest in a generalization of these types of algebra in which each individual…

We present a characterization of hyperbolicity for strongly continuous semigroups on Banach spaces in terms of Fourier multiplier properties of the resolvent of the generator. Hyperbolicity with respect to classical solutions is also…

We review and analyse techniques from the literature for extending a normed algebra, A to a normed algebra, B, so that B has interesting or desirable properties which A may lack. For example, B might include roots of monic polynomials over…

The prepotential of N=2* supersymmetric theories with unitary gauge groups in an Omega-background satisfies a modular anomaly equation that can be recursively solved order by order in an expansion for small mass. By requiring that S-duality…

It is known that a finite group G can only act freely on affine n-space if K has positive characteristic p and G is a p-group. In that case the group action is "non-linear" and the ring of regular functions must be a trace-surjective…

The symmetric group $\mathsf{S}_n$ and the partition algebra $\mathsf{P}_k(n)$ centralize one another in their actions on the $k$-fold tensor power $\mathsf{M}_n^{\otimes k}$ of the $n$-dimensional permutation module $\mathsf{M}_n$ of…

If $\mathfrak{g} \subseteq \mathfrak{h}$ is an extension of Lie algebras over a field $k$ such that ${\rm dim}_k (\mathfrak{g}) = n$ and ${\rm dim}_k (\mathfrak{h}) = n + m$, then the Galois group ${\rm Gal} \, (\mathfrak{h}/\mathfrak{g})$…