Related papers: Properties Preserved by Groupoid Equivalence
We present results on simplifying an acting group preserving properties of actions: transitivity, being a coset space and preserving a fixed equiuniformity in case of a $G$-Tychonoff space.
In this paper, we pose the concepts of pre-topological groups and some generalizations of pre-topological groups. First, we systematically investigate some basic properties of pre-topological groups; in particular, we prove that each…
A locally compact groupoid is said to have the weak containment property if its full $C^*$-algebra coincides with its reduced one. This property is strictly weaker than amenability and is known to be equivalent to amenability for…
We show that important structural properties of C*-algebras and the multiplicity numbers of representations are preserved under Morita equivalence.
We study permutations on n elements preserving orientation (parity) of every subset of size k. We describe all groups of these permutations. Unexpectedly, these groups (except for some special cases) are either trivial, cyclic or dihedral.…
Transformation properties of a class of generalized Kawahara equations with time-dependent coefficients are studied. We construct the equivalence groupoid of the class and prove that this class is not normalized but can be presented as a…
In this paper, some more properties of the generalized principal pivot transform are derived. Necessary and sufficient conditions for the equality between Moore-Penrose inverse of a generalized principal pivot transform and its…
In this note we show that the known relation between double groupoids and matched pairs of groups may be extended, or seems to extend, to the triple case. The references give some other occurrences of double groupoids.
Here we have investigated a few properties of the eigenvalues of normalized (geometric) graph Laplacian in different graphs. Preservation of eigenvalue 1 from a particular subgraph to the entire graph, the spectrum of the graph constructed…
In this paper we present the example which proves that we can not conclude the geometrical equivalence of group representations from the corresponding action-type geometrical equivalence and group geometrical equivalence.
We show that any proper Lie groupoid admits a compatible (real) analytic structure.
We study the categorical properties of right-preordered groups, giving an explicit description of limits and colimits in this category, and studying some exactness properties. We show that, from an algebraic point of view, the category of…
We prove that rigid representations of the fundamental group of a surface into the group of oreintation-preserving homeomorphisms of the circle are geometric, thereby establishing a converse statement of a theorem by the first author.
We survey the symmetry preserving properties for the dual propinquity, under natural non-degeneracy and equicontinuity conditions. These properties are best formulated using the notion of the covariant propinquity when the symmetries are…
We use the technology of linking groupoids to show that equivalent groupoids have Morita equivalent reduced C*-algebras. This equivalence is compatible in a natural way in with the Equivalence Theorem for full groupoid C*-algebras.
Hahn groups endowed with the canonical valuation play a fundamental role in the classification of valued abelian groups. In this paper we study the group of valuation (respectively order) preserving automorphisms of a Hahn group $G$. Under…
We describe the point and contact equivalence groupoids of an important class of two-dimensional quasilinear hyperbolic equations. In particular, we prove that this class is normalized in the usual sense with respect to point…
For an orbifold, there is a notion of an orbifold embedding, which is more general than the one of sub-orbifolds. We develop several properties of orbifold embeddings. In the case of translation groupoids, we show that such a notion is…
We give a few properties equivalent to the Bloch-Kato conjecture (now the norm residue isomorphism theorem).
A locally compact groupoid is said to be exact if its associated reduced crossed product functor is exact. In this paper, we establish some permanence properties of exactness, including generalizations of some known results for exact…