Related papers: Another invariant for AT actions
We perform certain alternating binomial summations with parameters that occur in the analysis of algorithms. A combination of integral and special function and special number representations is used. The results are sufficiently general to…
Some groups of real analytic diffeomorphism act n-transitively for each finite n.
A class of parametric functions formed by alternating compositions of multivariate polynomials and rectification style monomial maps is studied (the layer-wise exponents are treated as fixed hyperparameters and are not optimized). For this…
A trivial bundle of regular connected invariant manifolds of a completely integrable Hamiltonian system can be provided with action-angle coordinates.
The paper presents a new algorithmic construction of a finite generating set of rational invariants for the rational action of an algebraic group on the affine space. The construction provides an algebraic counterpart of the moving frame…
Let $\mathcal{M}(n)$ be the subgroup of $GL(n,\mathbb{Z})$ generated by the particular involutions that are identical to the identity, except for a single line where $-1$ and $+1$ alternate. We study the properties of $\mathcal{M}(n)$, and…
In this paper, we study partial actions of groups on $R$-algebras, where $R$ is a commutative ring. We describe the partial actions of groups on the indecomposable algebras with enveloping actions. Then we work on algebras that can be…
Invariants withstand transformations and, therefore, represent the essence of objects or phenomena. In mathematics, transformations often constitute a group action. Since the 19th century, studying the structure of various types of…
In this note we survey recent results on automorphisms of affine algebraic varieties, infinitely transitive group actions and flexibility. We present related constructions and examples, and discuss geometric applications and open problems.
Differential invariants of a (pseudo)group action can vary when restricted to invariant submanifolds (differential equations). The algebra is still governed by the Lie-Tresse theorem, but may change a lot. We describe in details the case of…
We construct a family of groups from suitable higher rank graphs which are analogues of the finite symmetric groups. We introduce homological invariants showing that many of our groups are, for example, not isomorphic to $nV$, when $n \geq…
We establish analogues in the context of group actions or group representations of some classical problems and results in additive combinatorics of groups. We also study the notion of left invariant submodular function defined on power sets…
To any Hamiltonian action of a reductive algebraic group $G$ on a smooth irreducible symplectic variety $X$ we associate certain combinatorial invariants: Cartan space, Weyl group, weight and root lattices. For cotangent bundles our…
We review computations of joint invariants on a linear symplectic space, discuss variations for an extension of group and space and relate this to other equivalence problems and approaches, most importantly to differential invariants.
We say that a group G acts infinitely transitively on a set X if for every integer m the induced diagonal action of G is transitive on the cartesian mth power of X with the diagonals removed. We describe three classes of affine algebraic…
An action of a group $G$ is highly transitive if $G$ acts transitively on $k$-tuples of distinct points for all $k \geq 1$. Many examples of groups with a rich geometric or dynamical action admit highly transitive actions. We prove that if…
This paper is a survey of our recent work on operator algebras associated to dynamical systems that lead to classification results for the systems in terms of algebraic invariants of the operator algebras.
We investigate continuous transitive actions of semitopological groups on spaces, as well as separately continuous transitive actions of topological groups.
We here present rudiments of an approach to geometric actions in noncommutative algebraic geometry, based on geometrically admissible actions of monoidal categories. This generalizes the usual (co)module algebras over Hopf algebras which…
We study higher rank Cartan actions on compact manifolds preserving an ergodic measure with full support. In particular, we classify actions by $\R ^k$ with $k \geq 3$ whose one-parameter groups act transitively as well as nondegenerate…