On identifying sheaves and bundles of topological algebras

• Autorzy: Kyriazis A.
• Języki publikacji: EN

Abstrakty

EN

In this paper we consider topological A-algebra sheaves on a topological space X, i.e., topological algebra sheaves on X with "coefficient sheaf" A. Thus, let Fi^(X) be the set of equivalence classes of locally free topological A-algebra sheaves of rank 1 on X, which is classified by H^1(X, A*), the 1-st cohomology set of X with coefficients in the topological group sheaf of units A* of A. Moreover,Fi_A(X) stands for the set of equivalence classes of topological algebra bundles on X of fibre type A, classified by H^1(X, Aut(A)), the 1-st cohomology set of X with coefficients in the topological group of automorphisms of A. Now, let A be a constant topological algebra sheaf whose fibre topological algebra A has continuous multiplication and inversion and also having locally equicontinuous Aut(A). Then, one gets the following bijections Fi(X) = H^1(X,A') =H^1(X,Aut(A))=Fi_A(X).

Słowa kluczowe

EN

topological A-algebra; free (of rank n) topological A-algebra sheaf; topological algebra bundles

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
• Rocznik: 2003
• Tom: [Z] 43(1)
• Strony: 95--104
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Kyriazis A.

• Department of Mathematics, University of Athens, Panepistimiopolis, 157 84 Athens, Greece,

Bibliografia

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• [2] G. E. Bredon, Sheaf Theory, McGraw-Hill, New York, (1967).
• [3] F. Hirzebruch, Topological Methods in Algebraic Geometry, Springer-Verlag, Berlin, (1978).
• [4] A. Kyriazis, On topological algebra bundles, J. Austr. Math. Soc. 43 (1987), 398-419.
• [5] A. Kyriazis, On tensor product α-algebra bundles, Proc. Intern. Conf. "Advances in the Theory of Fréchet Spaces", Istanbul, August 1988, NATO ASI Series C, Vol. 287, Kluwer Academic Publishers, Dordrecht, 1989, 223-234.
• [6] A. Kyriazis, On topological algebra sheaves, J. Austr. Math. Soc. 61 (1996), 14-29.
• [7] A. Mallios, Topological Algebras: Selected Topics, North Holland, Amsterdam, (1986).
• [8] A. Mallios, Geometry of Vector Sheaves An Axiomatic Approach to Differential Geometry (Vols. I, II), Kluwer Academic Publishers, Dordrecht, (1998).