Related papers: Multiplication of Weak Equivalence Classes May Be …

The theorems of M. Ratner, describing the finite ergodic invariant measures and the orbit closures for unipotent flows on homogeneous spaces of Lie groups, are extended for actions of subgroups generated by unipotent elements. More…

Let $\alpha: G\curvearrowright X$ be a continuous action of an infinite countable group on a compact Hausdorff space. We show that, under the hypothesis that the action $\alpha$ is topologically free and has no $G$-invariant regular Borel…

We introduce computable actions of computable groups and prove the following versions of effective Birkhoff's ergodic theorem. Let $\Gamma$ be a computable amenable group, then there always exists a canonically computable tempered two-sided…

In this paper, we investigate the computational complexity of isomorphism testing for finite groups and quasigroups, given by their multiplication tables. We crucially take advantage of their various decompositions to show the following: -…

We give a characterization of extremal irreducible discrete subfactors $(N\subseteq M, E)$ where $N$ is type ${\rm II}_1$ in terms of connected W*-algebra objects in rigid C*-tensor categories. We prove an equivalence of categories where…

The equivariant $K$-theory of the semi-infinite flag manifold, as developed recently by Kato, Naito, and Sagaki, carries commuting actions of the nil-double affine Hecke algebra (nil-DAHA) and a $q$-Heisenberg algebra. The action of the…

When one studies the structure (e.g. graded ideals, graded subspaces, radicals, ...) or graded polynomial identities of graded algebras, the grading group itself does not play an important role, but can be replaced by any other group that…

We demonstrate a relative solidity property for the product of a nonamenable biexact group with an arbitrary infinite group in the measure equivalence setting. Among other applications, we obtain the following unique product decomposition…

Let $(X,T)$ be a Cantor minimal system, and let $\Gamma$ denote either its associated topological full group or the full group of a Bratteli diagram associated with $(X,T)$. In this paper we describe the structure of indecomposable…

Let \alpha_0 be an affine action of a discrete group \Gamma on a compact homogeneous space X and \alpha_1 a smooth action of \Gamma on X which is C^1-close to \alpha_0. We show that under some conditions, every topological conjugacy between…

Let $\Gamma$ be a group acting on a scheme $X$ and on a Lie superalgebra $\mathfrak{g}$, both defined over an algebraically closed field of characteristic zero $\Bbbk$. The corresponding equivariant map superalgebra $M(\mathfrak{g},…

We study the critical exponents of discrete subgroups of a higher rank semi-simple real linear Lie group $G$. Let us fix a Cartan subspace $\mathfrak a\subset \mathfrak g$ of the Lie algebra of $G$. We show that if $\Gamma< G$ is a discrete…

Let G be a complete Kac-Moody group of rank n \geq 2 over the finite field of order q, with Weyl group W and building \Delta. We first show that if W is right-angled, then for all q \neq 1 mod 4 the group G admits a cocompact lattice \Gamma…

In this paper, we study almost finiteness and almost finiteness in measure of non-free actions. Let $\alpha:G\curvearrowright X$ be a minimal action of a locally finite-by-virtually $\mathbb{Z}$ group $G$ on the Cantor set $X$. We prove…

Let $\Gamma$ be a compact Polish group of finite topological dimension. For a countably infinite subset $S\subseteq \Gamma$, a domatic $\aleph_0$-partition (for its Schreier graph on $\Gamma$) is a partial function…

Working within the framework of free actions of countable amenable groups on compact metrizable spaces, we show that the small boundary property is equivalent to a density version of almost finiteness, which we call almost finiteness in…

The weak operator topology closed operator algebra on $L^2(R)$ generated by the one-parameter semigroups for translation, dilation and multiplication by $exp(i\lambda x), \lambda \geq 0$, is shown to be a reflexive operator algebra, in the…

Let $G$ be a connected semisimple real algebraic group. Assume that $G(\bb R)$ has no compact factors and let $\Gamma$ be a torsion-free uniform lattice subgroup of $G(\bb R)$. Then $\Gamma$ contains a malnormal abelian subgroup $A$. This…

We introduce a weak version of the classical length function, termed the weak length function, defined on subsets of $R$-modules over a unital ring $R$, and further consider the concept of mean weak length for $R\Gamma$-modules associated…

Suppose a group $\Gamma$ acts on a scheme $X$ and a Lie superalgebra $\mathfrak{g}$. The corresponding equivariant map superalgebra is the Lie superalgebra of equivariant regular maps from $X$ to $\mathfrak{g}$. We classify the irreducible…