# Representations of algebras by continuous sections

@article{Hofmann1972RepresentationsOA, title={Representations of algebras by continuous sections}, author={Karl Heinrich Hofmann}, journal={Bulletin of the American Mathematical Society}, year={1972}, volume={78}, pages={291-373} }

This survey is concerned with the representation of discrete rings and topological algebras (such as C*-algebras) by rings of continuous sections in sheaves of rings or fields of topological algebras.

## 91 Citations

Rings of continuous functions. Algebraic aspects

- Mathematics
- 1994

This survey paper is devoted to the algebraic theory of rings of continuous functions. The author considers the relationship between topological spaces and the corresponding rings of continuous…

Multiplier algebras, Banach bundles, and one-parameter semigroups

- Mathematics
- 1999

Several results are proved concerning representations of multiplier algebras
that arise as extensions of representations of underlying Banach algebras.
These results are then used to rederive…

Specification of topological spaces by algebraic systems of continuous functions

- Mathematics
- 1991

This survey presents results on specification of topological spaces by various algebraic structures of continuous functions. Results are presented on specification of E-compact spaces by general…

Sheaves of C*‐algebras

- Mathematics, Chemistry
- 2010

We develop the basics of a theory of sheaves of C*‐algebras and, in particular, compare it to the existing theory of C*‐bundles. The details of two fundamental examples, the local multiplier sheaf…

C*-bundle approach to a local principle

- Mathematics
- 2005

We propose a local principle which gives the global description of the algebra under study in terms of continuous sections of a certain canonically defined C∗-bundle.

The Spectral Radius in C0(X)-Banach Algebras

- Mathematics
- 2011

The spectral radius of an element of aC0(X)-Banach algebra can be calculated as the supremum of the spectral radii in the fibres. As a consequence, calculations in K-theory for such algebras can…

SYSTEMS OF CONTINUOUS FUNCTIONS

- Mathematics
- 1990

This survey presents results on specification of topological spaces by various algebraic structures of continuous functions. Results are presented on specification of E, compact spaces by general…

C*-algebras of Clifford semigroups

- Mathematics
- 1989

We investigate algebras associated with a (discrete) Clifford semigroup S =∪ { G e : e ∈ E {. We show that the representation theory for S is determined by an enveloping Clifford semigroup UC(S) =∪ {…

Convolution operators on standard CR-manifolds II. Algebras of convolution operators on the Heisenberg group

- Mathematics
- 1994

Various algebras generated by one-sided and two-sided convolution operators with homogeneous kernels and on the Heisenberg group are considered. Isomorphic description of these algebras are given.…

## References

SHOWING 1-10 OF 76 REFERENCES

On the Representation of Modules by Sheaves of Factor Modules

- MathematicsCanadian Mathematical Bulletin
- 1971

Throughout this paper we consider associative rings with unity elements. In §1 various results on the representation of rings by rings of sections of special rings are compared. In particular, it is…

On Functional Representations of a Ring without Nilpotent Elements

- MathematicsCanadian Mathematical Bulletin
- 1971

In [3, p. 149], J. Lambek gives a proof of a theorem, essentially due to Grothendieck and Dieudonne, that if R is a commutative ring with 1 then R is isomorphic to the ring of global sections of a…

The Space of Minimal Prime Ideals of a Commutative Ring

- Mathematics
- 1965

Introduction. Of the various spaces of ideal of rings that have been studied (see [1 ], for example) we are focusing attention on the space of minimal prime ideals because of its special role in the…

Rings with orthogonality relations

- MathematicsBulletin of the Australian Mathematical Society
- 1971

The rings of this paper are assumed to have relations of orthogonality defined on them. Such relations are uniquely determined by complete boolean algebras of ideals. Using the Stone space of these…

Vector bundles and projective modules

- Mathematics
- 1962

Serre [9, ?50] has shown that there is a one-to-one correspondence between algebraic vector bundles over an affine variety and finitely generated projective modules over its coordinate ring. For some…

TOPOLOGICAL REPRESENTATION OF C*-ALGEBRAS

- Mathematics
- 1962

Let A be a C*-algebra, ίl the structure space of A, i.e. the space of all primitive ideals in A with hull-kernel topology. At every point P of ί l we associate a primitive C^-algebra A/P (which we…

A sheaf-theoretic duality theory for cylindric algebras

- Mathematics
- 1972

Stone's duality between Boolean algebras and Boolean spaces is extended to a dual equivalence between the category of all ^dimensional cylindric algebras and a certain category of sheaves of such…

Prime ideal structure in commutative rings

- Mathematics
- 1969

0. Introduction. Let ' be the category of commutative rings with unit, and regard Spec (as in [1]) as a contravariant functor from ' to g$7 the category of topological spaces and continuous maps. The…

The Minimal Prime Spectrum of a Commutative Ring

- MathematicsCanadian Journal of Mathematics
- 1971

We call a topological space X minspectral if it is homeomorphic to the space of minimal prime ideals of a commutative ring A in the usual (hull-kernel or Zariski) topology (see [2, p. 111]). Note…