相关论文: Host Algebras

A group, defined as set with associative multiplication and inverse, is a natural structure describing the symmetry of a space. The concept of group generalizes to group objects internal to other categories than sets. But there are yet more…

We describe representations of groupoid C*-algebras on Hilbert modules over arbitrary C*-algebras by a universal property. For Hilbert space representations, our universal property is equivalent to Renault's Integration-Disintegration…

We consider operators on $L^2$ spaces that expand the support of vectors in a manner controlled by some constraint function. The primary objects of study are $\mathrm C^*$-algebras that arise from suitable families of constraints, which we…

In recent times a new kind of representations has been used to describe superselection sectors of the observable net over a curved spacetime, taking into account of the effects of the fundamental group of the spacetime. Using this notion of…

We analzye Rieffel's construction of generalized fixed point algebras in the setting of group actions on Hilbert modules. Let G be a locally compact group acting on a C*-algebra B. We construct a Hilbert module F over the reduced crossed…

This work provides a generalization of the Gelfand duality to the context of noncommutative locally $C^*$ algebras. Using a reformulation of a theorem proven by Dauns and Hofmann in the 60's we show that every locally $C^*$ algebra can be…

Let $G$ be a locally compact groupoid. If $X$ is a free and proper $G$-space, then $(X*X)/G$ is a groupoid equivalent to $G$. We consider the situation where $X$ is proper but no longer free. The formalism of groupoid C*-algebras and their…

Let $\Theta$ be a variety of algebras. In every $\Theta$ and every algebra $H$ from $\Theta$ one can consider algebraic geometry in $\Theta$ over $H$. We consider also a special categorical invariant $K_\Theta (H)$ of this geometry. The…

In the present paper the notion of a Hilbert module over a locally C*-algebra is discussed and some results are obtained on this matter. In particular, we give a detailed proof of the known result that the set of adjointable endomorphisms…

The completion of a (normed) $C^*$-algebra $A_0[\| \cdot \|_0]$ with respect to a locally convex topology $\tau$ on $A_0$ that makes the multiplication of $A_0$ separately continuous is, in general, a quasi *-algebra, and not a locally…

We prove that if a connected and simply connected Lie group $G$ admits connected closed normal subgroups $G_1\subseteq G_2\subseteq \cdots \subseteq G_m=G$ with $\dim G_j=j$ for $j=1,\dots,m$, then its group $C^*$-algebra has closed…

Let $G$ be a connected complex algebraic group and $A$ a connected abelian algebraic group endowed with an algebraic action of $G$ by group automorphisms. In the present note we describe the abelian group $\Ext_{alg}(G,A)$ of algebraic…

The construction of the C*-algebra associated to a directed graph $E$ is extended to incorporate a family $C$ consisting of partitions of the sets of edges emanating from the vertices of $E$. These C*-algebras $C^*(E,C)$ are analyzed in…

The study of different types of ideals in non self-adjoint operator algebras has been a topic of recent research. This study focuses on principal ideals in subalgebras of groupoid C*-algebras. An ideal is said to be principal if it is…

For a locally convex $^*$-algebra $A$ equipped with a fixed continuous $^*$-character $\varepsilon$, we define a cohomological property, called property $(FH)$, which is similar to character amenability. Let $C_c(G)$ be the space of…

Let W be a finite Coxeter group. We define its Hecke-group algebra by gluing together appropriately its group algebra and its 0-Hecke algebra. We describe in detail this algebra (dimension, several bases, conjectural presentation,…

We show that the basic categorical concept of an S-algebra as derived from the theory of Segal's Gamma-sets provides a unifying description of several constructions attempting to model an algebraic geometry over the absolute point. It…

Presented is a structure theorem for the Leibniz Homology, HL_*, of an Abelian extension of a simple real Lie algebra g. As applications, results are stated for affine extensions of the classical Lie algebras sl_n(R), so_n(R), and sp_n(R).…

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 notion of a $F$-manifold algebras is an algebraic description of a $F$-manifold. In this paper, we introduce the notion of Hom-$F$-manifold algebras which is generalisation of $F$-manifold algebras and Hom-Poisson algebras. We develop…