Related papers: Expansive Lie Group Actions
We survey some of the known criteria for expansiveness of principal algebraic actions of countably infinite discrete groups. In the special case of the discrete Heisenberg group we propose a new approach to this problem based on Allan's…
We introduce notions of absolutely non-free and perfectly non-free group actions and use them to study the associated unitary representations. We show that every weakly branch group acts absolutely non-freely on the boundary of the…
The factorization form of the integrands in the Cachazo-He-Yuan (CHY) formalism makes the generalized Kawai-Lewellen-Tye (KLT) relations manifest, thus amplitudes of one theory can be expanded in terms of the amplitudes of another theory.…
In this survey, we discuss a series of linearization problems--for Poisson structures, Lie algebroids, and Lie groupoids. The last problem involves a conjecture on the structure of proper groupoids. Attempting to prove this by the method of…
Lie groups and quantum algebras are connected through their common universal enveloping algebra. The adjoint action of Lie group on its algebra is naturally extended to related q-algebra and q-coalgebra. In such a way, quantum structure can…
For a locally compact metrizable group $G$, we consider the action of ${\rm Aut}(G)$ on ${\rm Sub}_G$, the space of all closed subgroups of $G$ endowed with the Chabauty topology. We study the structure of groups $G$ admitting automorphisms…
In this paper, we define and study weak expansive and expansive measures for pseudogroups, these two notions appear when analyzing the role of the generating set. We investigate the relations between such properties. We also provide a…
We study the behaviors of quantum groups under an edge contraction. We show that there exists an explicit embedding induced by an edge contraction operation. We further conjecture that this explicit embedding is a section of an explicit…
In the study of aperiodic order via dynamical methods, topological entropy is an important concept. In this paper, parts of the theory, like Bowen's formula for fibre wise entropy or the independence of the definition from the choice of a…
We describe a natural topological generalization of edge expansion for graphs to regular CW complexes and prove that this property holds with high probability for certain random complexes.
We describe the action of the infinite-dimensional Lie algebra $W_{1+\infty}$ and its B-type analogue on Schur and Schur Q-functions, respectively, using formal distributions framework. We observe an interesting self-duality property…
We give an explicit description of the category of central extensions of a group scheme by a sheaf of Abelian groups. Based on this, we describe a framework for computing with central extensions of finite commutative group schemes, torsors…
In this paper we study Zimmer's conjecture for $C^1$ actions of lattice subgroup of a higher-rank simple Lie group with finite center on compact manifolds. We show that when the rank of an uniform lattice is larger than the dimension of the…
The notion of expansivity and its generalizations (measure expansive, measure positively expansive, continuum-wise expansive, countably-expansive) are well known for deterministic systems and can be a useful property for studying…
In this paper we study holomorphic actions of the complex multiplicative group on complex manifolds around a singular (fixed) point. We prove linearization results for the germ of action and also for the whole action under some conditions…
We discuss a general methodology to provide rigid, off-shell matter multiplets and actions for recently constructed non-relativistic superalgebras. The technique is based on the Lie algebra expansion, which, in the context of supersymmetry,…
We prove that every expansive continuous action with the weak specification property of an amenable group $G$ on a compact Hausdorff space $X$ has the Myhill property, i.e., every pre-injective continuous self-mapping of $X$ commuting with…
Holomorphic functions of exponential type on a complex Lie group $G$ (introduced by Akbarov) form a locally convex algebra, which is denoted by $\cO_{exp}(G)$. Our aim is to describe the structure of $\cO_{exp}(G)$ in the case when $G$ is…
Edgeworth expansions for random walks on covering graphs with groups of polynomial volume growths are obtained under a few natural assumptions. The coefficients appearing in this expansion depends on not only geometric features of the…
We give a characterisation of central extensions of a Lie group G by the non-zero complex numbers in terms of a differential two-form on G and a differential one-form on GxG. This is applied to the case of the central extension of the loop…