相关论文: The Picard groupoid in deformation quantization

The goal of the present paper is to introduce a smaller, but equivalent version of the Deligne-Hinich-Getzler $\infty$-groupoid associated to a homotopy Lie algebra. In the case of differential graded Lie algebras, we represent it by a…

We make use of a well-know deformation of the Poincar\'e Lie algebra in $p+q+1$ dimensions ($p+q>0$) to construct the Poincar\'e Lie algebra out of the Lie algebras of the de Sitter and anti de Sitter groups, the generators of the…

Given a normal subgroup bundle $\mathcal A$ of the isotropy bundle of a groupoid $\Sigma$, we obtain a twisted action of the quotient groupoid $\Sigma/\mathcal A$ on the bundle of group $C^*$-algebras determined by $\mathcal A$ whose…

Let the groupoid $G$ with unit space $G^0$ act via a representation $\rho$ on a $C^*$-correspondence ${\mathcal H}$ over the $C_0(G^0)$-algebra $A$. By the universal property, $G$ acts on the Cuntz-Pimsner algebra ${\mathcal O}_{\mathcal…

Let $(K,\mathcal O,k)$ be a $p$-modular system and assume $k$ is algebraically closed. We show that if $\Lambda$ is an $\mathcal O$-order in a separable $K$-algebra, then $\textrm{Pic}_{\mathcal O}(\Lambda)$ carries the structure of an…

The Brauer group of a commutative ring is an important invariant of a commutative ring, a common journeyman to the group of units and the Picard group. Burnside rings of finite groups play an important role in representation theory, and…

First, I construct an isomorphism between the categories of (topological) groups of nilpotency class 2 with 2-divisible center and (topological) Lie rings of nilpotency class 2 with 2-divisible center. That isomorphism allows us to…

The purpose of this paper is to develop a deformation theory controlled by pre-Lie algebras with divided powers over a ring of positive characteristic. We show that every differential graded pre-Lie algebra with divided powers comes with…

In a previous paper we generalized the theory of W*-modules to the setting of modules over nonselfadjoint dual operator algebras, obtaining the class of weak*-rigged modules. At that time we promised a forthcoming paper devoted to other…

Let $(X,\bullet )$ be a groupoid (binary algebra) and $Bin(X\dot{)}$ denote the collection of all groupoids defined on $X$. We introduce two methods of factorization for this binary system under the binary groupoid product \textquotedblleft…

A theorem of Muhly-Renault-Williams states that if two locally compact groupoids with Haar system are Morita equivalent, then their associated convolution C*-algebras are strongly Morita equivalent. We give a new proof of this theorem for…

We investigate the concept of definable, or inner, automorphism in the logical setting of partial Horn theories. The central technical result extends a syntactical characterization of the group of such automorphisms (called the covariant…

By a ring groupoid we mean an animated ring whose i-th homotopy groups are zero for all i>1. In this expository note we give an elementary treatment of the (2,1)-category of ring groupoids (i.e., without referring to general animated rings…

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…

As a sequel to our proof of the analog of Serre's conjecture for function fields in Part I of this work, we study in this paper the deformation rings of $n$-dimensional mod $\ell$ representations $\rho$ of the arithmetic fundamental group…

Kaplansky introduced the notions of CCR and GCR $C^*$-algebras because they have a tractable representation theory. Many years later, he introduced the notions of CCR and GCR rings. In this paper we characterize when the algebra of an ample…

We use braided groups to introduce a theory of $*$-structures on general inhomogeneous quantum groups, which we formulate as {\em quasi-$*$} Hopf algebras. This allows the construction of the tensor product of unitary representations up to…

We introduce partial representation of a finite groupoid $G$ on an algebra $A$ and show that the partial groupoid representations of $G$ are in one-to-one correspondence with the representations of the algebra generated by the Birget-Rhodes…

We show that important structural properties of C*-algebras and the multiplicity numbers of representations are preserved under Morita equivalence.

Though the irreducible representations of the Poincare' group form the groundwork for the formulation of relativistic quantum theories of a particle, robust classes of such representations are missed in current formulations of these…