Fibre tensor product bundles

Gelbaum, Bernard R.; Kyriazis, Athanasios

doi:10.1090/s0002-9939-1985-0776201-1

Cited by 5 publications

(1 citation statement)

References 4 publications

(4 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In addition the preceding specializes to the standard result that 3Jf(^c(X)) and X are homeomorphic, when X is a completely regular space [9]. A similar result has been given in [6] by considering fibre tensor product bundles. In a future publication we hope to extend Theorem 4.1 to the case of a non compact base space X.…”

mentioning

confidence: 67%

On Topological Algebra Bundles

Kyriazia

1987

J Aust Math Soc A

View full text Add to dashboard Cite

show abstract

mentioning

confidence: 67%

On Topological Algebra Bundles

Kyriazia

1987

J Aust Math Soc A

View full text Add to dashboard Cite

show abstract

On Fibre Tensor Product Bundles

Kyriazis

1992

Mathematische Nachrichten

Self Cite

View full text Add to dashboard Cite

We consider here an improved and generalized form of fibre tensor product bundles, objects locally looking like tensor products. A certain subclass of such bundles is also characterized as an appropriate type of locally trivial fibre bundles.Fibre tensor product bundles have been studied in [1]. For convenience, we first recall the relevant definition: That is, suppose that A, B are unital locally convex algebras such that A has a compact spectrum %Jl(A) [3]. Thus, a fibre tensor product bundle is defined by the following data:1) There exists a finite set {Ii} of closed 2-sided ideals of A with compact hulls Fi = h(li) c %Jl(A) and non-empty interiors Pi = U i such that ! I l l @ )2) There exists an Aut (B)-cocycle (hij) associated to 'ill = (Ui) (i.e., (hij) E Z1(%, Aut (B))) such that each h, has a unique continuous extension hij: F i n F j -+ A u t ( B ) as an (Aut (B)-) cocycle.3) There exists a closed subalgebra D of S = 1 A/I, @B consisting of all those C a, 0 bin E S with C S i n c f ) bin = 1 ciin(f) h i j ( f ) bin, for some f~ Fin Fj.The purpose of this note is to improve and also generalize the previous setting: This is accomplished first by considering topological algebras, not necessarily locally convex. Then, instead of the group Aut ( B ) of C-automorphisms of B, one considers a topological group G acting continuously and effectively on B. (I am indebted for this last point of view to Professor A. MALLIOS). Furthermore, the family { I , } of ideals of A is not-necessarily finite as was the case in 1) above, nor m ( A ) is compact.Yet we remark that the above condition 3) is actually redundant (cf. (1.4)). Finally, the above algebra D may be regarded as an abstract version of the algebra of sections of an algebra bundle (see SCHOLIUM 1.1).As a consequence, our main result (Theorem 4.2) identifies a subcategory (cf. (1.3) and Theorem 2.1) of the category of fibre tensor product bundles with a subcategory

show abstract

Bibliography

1988

Pure and Applied Mathematics

View full text Add to dashboard Cite

Fibre tensor product bundles

Abstract: In analogy with fibre bundles, which are locally Cartesian products, fibre tensor product bundles are objects that are locally tensor products. These can be patched together via transition maps, etc., into an object very similar to the set of sections of a locally convex algebra bundle.

Cited by 5 publications

References 4 publications

On Topological Algebra Bundles

On Topological Algebra Bundles

On Fibre Tensor Product Bundles

Bibliography

Contact Info

Product

Resources

About