相关论文: On the flag structure and classification of the ho…
For $\Omega\subseteq \mathbb{C}$ a connected open set, and ${\mathcal U}$ a unital $C^*$-algebra, let ${\mathcal I} ({\mathcal U})$ and ${\mathcal P}({\mathcal U})$ denote the sets of all idempotents and projections in ${\mathcal U}$…
In this paper, a new criterion for the similarity of commuting tuples of operators on Hilbert spaces is introduced. As an application, we obtain a geometric similarity invariant of tuples in the Cowen-Douglas class which gives a partial…
The explicit description of homogeneous operators and localization of a Hilbert module naturally leads to the definition of a class of Cowen-Douglas operators possessing a flag structure. These operators are irreducible. We show that the…
In this paper we study quasi-homogeneous operators, which include the homogeneous operators, in the Cowen-Douglas class. We give two separate theorems describing canonical models (with respect to equivalence under unitary and invertible…
We construct Koppelman formulas on manifolds of flags in $\C^N$ for forms with values in any holomorphic line bundle as well as in the tautological vector bundles and their duals. As an application we obtain new explicit proofs of some…
In the standard category of directed graphs, graph morphisms map edges to edges. By allowing graph morphisms to map edges to finite paths (path homomorphisms of graphs), we obtain an ambient category in which we determine subcategories…
The study of Cowen-Douglas operators involves not only operator-theoretic tools but also complex geometry on holomorphic vector bundles. By leveraging the properties of holomorphic vector bundles, this paper investigates the cyclicity of…
A functor from the category of directed trees with inclusions to the category of commutative C*-algebras with injective *-homomorphisms is constructed. This is used to define a functor from the category of directed graphs with inclusions to…
We consider a subclass of the Cowen-Douglas class in which the problem of deciding whether two operators are similar becomes more manageable. A similarity criterion for Cowen-Douglas operators is known to be dependent on the trace of the…
Representations of $C^*$-algebras are realized on section spaces of holomorphic homogeneous vector bundles. The corresponding section spaces are investigated by means of a new notion of reproducing kernel, suitable for dealing with…
A new category of topological spaces with additional structures, called m-towers, is introduced. It is shown that there is a covariant functor which establishes a one-to-one correspondences between unital (resp. arbitrary) subhomogeneous…
Based on the Brieskorn-Slodowy-Grothendieck diagram, we write the holomorphic structures (or filtrations) of the ADE Lie algebra bundles over the corresponding type ADE flag varieties, over the cotangent bundles of these flag varieties, and…
In [11] the authors investigated a family of quotient Hilbert modules in the Cowen-Douglas class over the unit disk constructed from classical Hilbert modules such as the Hardy and Bergman modules. In this paper we extend the results to the…
We continue an analysis of representations of cylindrical functions and fluxes which are commonly used as elementary variables of Loop Quantum Gravity. We consider an arbitrary principal bundle of a compact connected structure group and…
The construction of a C*-algebra of a differential groupoid is presented. It is shown that it defines a covariant functor from the category of differential groupoids in a sense of S. Zakrzewski to the category of C*-algebras.
The explicit description of irreducible homogeneous operators in the Cowen-Douglas class and the localization of Hilbert modules naturally leads to the definition of a smaller class of Cowen-Douglas operators possessing a flag structure.…
We introduce a new class of C^*-algebras, which is a generalization of both graph algebras and homeomorphism C^*-algebras. This class is very large and also very tractable. We prove the so-called gauge-invariant uniqueness theorem and the…
We investigate the geometry of holomorphic curves and complex surfaces from the perspective of singularity theory. We show that, with a suitable choice of a complex bilinear symmetric form, the families of functions and mappings that…
This paper introduces the category of marked curved Lie algebras with curved morphisms, equipping it with a closed model category structure. This model structure is---when working over an algebraically closed field of characteristic…
We develop an algebraic version of Cartan method of equivalence or an analog of Tanaka prolongation for the (extrinsic) geometry of curves of flags of a vector space $W$ with respect to the action of a subgroup $G$ of the $GL(W)$. Under…