63,533 research outputs found
On the Fine-Structure of Regular Algebra
Regular algebra is the algebra of regular expressions as induced by regular language identity. We use Isabelle/HOL for a detailed systematic study of the regular algebra axioms given by Boffa, Conway, Kozen and Salomaa. We investigate the relationships between these systems, formalise a soundness proof for the smallest class (Salomaa’s) and obtain completeness for the largest one (Boffa’s) relative to a deep result by Krob. As a case study in formalised mathematics, our investigations also shed some light on the power of theorem proving technology for reasoning with algebras and their models, including proof automation and counterexample generation
A new description of equivariant cohomology for totally disconnected groups
We consider smooth actions of totally disconnected groups on simplicial complexes and compare
different equivariant cohomology groups associated to such actions. Our main result is that the
bivariant equivariant cohomology theory introduced by Baum and Schneider can be described using
equivariant periodic cyclic homology.
This provides a new approach to the construction of Baum and Schneider as well
as a computation of equivariant periodic cyclic homology for a natural class of examples.
In addition we discuss the relation between cosheaf homology and equivariant
Bredon homology.
Since the theory of Baum and Schneider generalizes cosheaf homology we finally see
that all these approaches to equivariant cohomology for totally disconnected
groups are closely related
Toric singularities revisited
In [Kat94b], Kato defined his notion of a log regular scheme and studied the
local behavior of such schemes. A toric variety equipped with its canonical
logarithmic structure is log regular. And, these schemes allow one to
generalize toric geometry to a theory that does not require a base field. This
paper will extend this theory by removing normality requirements.Comment: new longer introduction, other minor improvements, 35 page
Coactions of Hopf C*-bimodules
Coactions of Hopf C*-bimodules simultaneously generalize coactions of Hopf
C*-algebras and actions of groupoids. Following an approach of Baaj and
Skandalis, we construct reduced crossed products and establish a duality for
fine coactions. Examples of coactions arise from Fell bundles on groupoids and
actions of a groupoid on bundles of C*-algebras. Continuous Fell bundles on an
etale groupoid correspond to coactions of the reduced groupoid algebra, and
actions of a groupoid on a continuous bundle of C*-algebras correspond to
coactions of the function algebra.Comment: 44 pages, to appear in the Journal of Operator theor
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