Related papers: Groupoid cocycles and derivations
For a Lie groupoid there is an analytic index morphism which takes values in the $K-$theory of the $C^*$-algebra associated to the groupoid. This is a good invariant but extracting numerical invariants from it, with the existent tools, is…
For any Lie groupoid we construct an analytic index morphism taking values in a modified $K-theory$ group which involves the convolution algebra of compactly supported smooth functions over the groupoid. The construction is performed by…
In this article, we generalize the theory of discrete Lagrangian mechanics and variational integrators in two principal directions. First, we show that Lagrangian submanifolds of symplectic groupoids give rise to discrete dynamical systems,…
We study deformations of Lie groupoids by means of the cohomology which controls them. This cohomology turns out to provide an intrinsic model for the cohomology of a Lie groupoid with values in its adjoint representation. We prove several…
The Lie algebra of the Poincar\'e-Maxwell group is derived in a manner that provides the interpretation of the equations of motion. It is clarified that the dynamics obtained from the orbit method is exactly equivalent to the classical…
A categorical theory for the discretization of a large class of dynamical systems with variable coefficients is proposed. It is based on the existence of covariant functors between the Rota category of Galois differential algebras and…
There is a simple and natural quantization of differential forms on odd Poisson supermanifolds, given by the relation [f,dg]={f,g} for any two functions f and g. We notice that this non-commutative differential algebra has a geometrical…
The multiplicative structure of the trivial symplectic groupoid over $\mathbb R^d$ associated to the zero Poisson structure can be expressed in terms of a generating function. We address the problem of deforming such a generating function…
We study equivariant birationality from the perspective of derived categories. We produce examples of nonlinearizable but stably linearizable actions of finite groups on smooth cubic fourfolds.
Given an infinite, compact, monothetic group $G$ we study decompositions and structure of unbounded derivations in a crossed product C$^*$-algebra $C(G)\rtimes\Z$ obtained from a translation on $G$ by a generator of a dense cyclic subgroup.…
We discuss a concept of loopoid as a non-associative generalization of (Brandt) groupoid. We introduce and study also an interesting class of more general objects which we call semiloopoids. A differential version of loopoids is intended as…
Suppose $\mathcal{G}$ is a second-countable locally compact Hausdorff \'{e}tale groupoid, $G$ is a discrete group containing a unital subsemigroup $P$, and $c:\mathcal{G}\rightarrow G$ is a continuous cocycle. We derive conditions on the…
The Galois theory of logarithmic differential equations with respect to relative D-groups in partial differential-algebraic geometry is developed.
We define a cocycle on the group of symplectic diffeomorphisms of a symplectic manifold and investigate its properties. The main applications are concerned with symplectic actions of discrete groups. For example, we give an alternative…
These lectures concern basic aspects of the theory of semigroups of endomorphisms of type $I$ factors that relate to causal dynamics, dilation theory, and the problem of classifying $E_0$-semigroups up to cocycle conjugacy. We give only a…
The theory of non symmetric Dirichlet forms is generalized to the non abelian setting, also establishing the natural correspondences among Dirichlet forms, sub-Markovian semigroups and sub-Markovian resolvents within this context. Examples…
In this thesis we give a construction of cyclic cocycles on convolution algebras twisted by gerbes over discrete translation groupoids. In his seminal book, Connes constructs a map from the equivariant cohomology of a manifold carrying the…
We construct an algebra of pseudodifferential operators on each groupoid in a class that generalizes differentiable groupoids to allow manifolds with corners. We show that this construction encompasses many examples. The subalgebra of…
We investigate deformations of skew group algebras that arise from a finite cyclic group acting on a polynomial ring in positive characteristic, where characteristic divides the order of the group. We allow deformations which deform both…
We introduce a new approach to constructing derived deformation groupoids, by considering them as parameter spaces for strong homotopy bialgebras. This allows them to be constructed for all classical deformation problems, such as…