scholarly journals Projective Modules Over Quantum Projective Line

2017 ◽  
Vol 28 (03) ◽  
pp. 1750022 ◽  
Author(s):  
Albert Jeu-Liang Sheu
Keyword(s):  
Projective Line ◽  
Complete Classification ◽  
Projective Modules ◽  
C Algebra ◽  
Isomorphism Classes ◽  
Complex Projective Spaces ◽  
Algebra Approach ◽  
Quantum Spheres ◽  
Complex Projective

Taking a groupoid C*-algebra approach to the study of the quantum complex projective spaces [Formula: see text] constructed from the multipullback quantum spheres introduced by Hajac and collaborators, we analyze the structure of the C*-algebra [Formula: see text] realized as a concrete groupoid C*-algebra, and find its [Formula: see text]-groups. Furthermore, after a complete classification of the unitary equivalence classes of projections or equivalently the isomorphism classes of finitely generated projective modules over the C*-algebra [Formula: see text], we identify those quantum principal [Formula: see text]-bundles introduced by Hajac and collaborators among the projections classified.

CLASSIFICATION OF REAL ALGEBRAIC VECTOR BUNDLES OVER THE REAL ANISOTROPIC CONIC

2005 ◽  
Vol 16 (10) ◽  
pp. 1207-1220 ◽  
Author(s):  
INDRANIL BISWAS ◽  
D. S. NAGARAJ
Keyword(s):  
Vector Bundles ◽  
Complete Classification ◽  
Real Numbers ◽  
The Real ◽  
Isomorphism Classes ◽  
Algebraic Vector

We give a complete classification of isomorphism classes of real algebraic vector bundles over the scheme defined by a nondegenerate anisotropic conic defined over the field of real numbers.

COMPLETE CLASSIFICATION OF SPECTRAL OPERATOR ALGEBRAS ASSOCIATED WITH DIVISIBLE PRODUCT SYSTEMS

1998 ◽  
Vol 09 (08) ◽  
pp. 923-943
Author(s):  
MASAYASU AOTANI
Keyword(s):  
Operator Algebras ◽  
Banach Algebras ◽  
Complete Classification ◽  
Isomorphism Problem ◽  
Spectral Operator ◽  
Product System ◽  
C Algebra ◽  
Product Systems ◽  
Algebraic Representations

Completely spatial E0-semigroups constitute the most important class of E0-semigroups. Each completely spatial E0-semigroup α induces a divisible product system Eα and a C*-algebra C*(Eα) called the spectral C*-algebra. It has been shown by Arveson that Eα and Eβ are isomorphic as product systems if and only if α and β are cocycle conjugate. He has also proved that representations of E correspond bijectively to ordinary C*-algebraic representations of C*(E). While it is trivial to show that C*(Eα) and C*(Eβ) are isomorphic if the underlying product systems Eα and Eβ are isomorphic, it is not known whether C*(Eα) and C*(Eβ) can be isomorphic when Eα and Eβ are not. In this paper we will consider a related isomorphism problem among the Banach algebras, known as spectral operator algebras, associated with divisible product systems. It will be shown that the spectral operator algebras [Formula: see text] and [Formula: see text] are isomorphic if and only if Eα and Eβ are isomorphic. This classification is important as C*(E) is a hereditary subalgebra of the C*-algebra [Formula: see text] generated by [Formula: see text].

On Lagrangian embeddings into the complex projective spaces

2016 ◽  
Vol 27 (05) ◽  
pp. 1650044 ◽  
Author(s):  
Toru Yoshiyasu
Keyword(s):  
Projective Line ◽  
Symplectic Manifolds ◽  
Product Formula ◽  
Complex Projective Plane ◽  
Lagrangian Immersion ◽  
Complex Projective Spaces ◽  
Sum Formula ◽  
Simply Connected ◽  
Lagrangian Embedding ◽  
Complex Projective

We prove that for any closed orientable connected [Formula: see text]-manifold [Formula: see text] and any Lagrangian immersion of the connected sum [Formula: see text] either into the complex projective [Formula: see text]-space [Formula: see text] or into the product [Formula: see text] of the complex projective line and the complex projective plane, there exists a Lagrangian embedding which is homotopic to the initial Lagrangian immersion. To prove this, we show that Eliashberg–Murphy’s [Formula: see text]-principle for Lagrangian embeddings with a concave Legendrian boundary and Ekholm–Eliashberg–Murphy–Smith’s [Formula: see text]-principle for self-transverse Lagrangian immersions with the minimal or near-minimal number of double points hold for six-dimensional simply connected compact symplectic manifolds.

A Complete Classification of AI Algebras with the Ideal Property

2011 ◽  
Vol 63 (2) ◽  
pp. 381-412 ◽  
Author(s):  
Kui Ji ◽  
Chunlan Jiang
Keyword(s):  
Inductive Limit ◽  
Complete Classification ◽  
C Algebra ◽  
Ideal Property ◽  
Positive Integers ◽  
The Ideal

Abstract Let A be an AI algebra; that is, A is the C*-algebra inductive limit of a sequencewhere are [0, 1], kn, and [n, i] are positive integers. Suppose that A has the ideal property: each closed two-sided ideal of A is generated by the projections inside the ideal, as a closed two-sided ideal. In this article, we give a complete classification of AI algebras with the ideal property.

scholarly journals Quadratic maps with a periodic critical point of period 2

2016 ◽  
Vol 13 (06) ◽  
pp. 1393-1417
Author(s):  
Jung Kyu Canci ◽  
Solomon Vishkautsan
Keyword(s):  
Critical Point ◽  
Projective Line ◽  
Periodic Points ◽  
Complete Classification ◽  
Quadratic Polynomials ◽  
Quadratic Maps ◽  
Period 2 ◽  
Classification Of Graphs

We provide a complete classification of possible graphs of rational preperiodic points of endomorphisms of the projective line of degree 2 defined over the rationals with a rational periodic critical point of period 2, under the assumption that these maps have no periodic points of period at least 7. We explain how this extends results of Poonen on quadratic polynomials. We show that there are exactly 13 possible graphs, and that such maps have at most nine rational preperiodic points. We provide data related to the analogous classification of graphs of endomorphisms of degree 2 with a rational periodic critical point of period 3 or 4.

scholarly journals Classification of certain inductive limit actions of compact groups on af algebras

2020 ◽  
pp. 2050128
Author(s):  
Qingyun Wang
Keyword(s):  
Compact Group ◽  
Inductive Limit ◽  
Complete Classification ◽  
Compact Groups ◽  
C Algebra ◽  
Finite Dimensional ◽  
K Theory ◽  
Af Algebras

Let [Formula: see text] be an AF algebra, [Formula: see text] be a compact group. We consider inductive limit actions of the form [Formula: see text], where [Formula: see text] is an action on the finite-dimensional C*-algebra [Formula: see text] which fixes each matrix summand. We give a complete classification up to conjugacy of such actions using twisted equivariant K-theory.

scholarly journals GROTHENDIECK GROUP INVARIANTS FOR PARTLY SELF-ADJOINT OPERATOR ALGEBRAS

2000 ◽  
Vol 11 (01) ◽  
pp. 41-64 ◽  
Author(s):  
S. C. POWER
Keyword(s):  
Operator Algebras ◽  
Adjoint Operator ◽  
Grothendieck Group ◽  
Complete Classification ◽  
Fundamental Relation ◽  
General Operator ◽  
C Algebra ◽  
Incidence Algebras ◽  
Direct Limits

Partially ordered Grothendieck group invariants are introduced for general operator algebras and used in the classification of direct systems and direct limits of finite-dimensional complex incidence algebras with common reduced digraph H (systems of H-algebras). In particular the dimension distribution groupG (A; C), defined for an operator algebra A and a self-adjoint subalgebra C, generalizes both the K0 group of a σ-unital C*-algebra B and the spectrum (fundamental relation) R(A) of a regular limit A of triangular digraph algebras. This invariant is more economical and computable than the regular Grothendieck group [Formula: see text] which nevertheless forms the basis for a complete classification of regular systems of H-algebras.

Sign in / Sign up

Export Citation Format

Share Document