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1999 | 137 | 1 | 1-31
Tytuł artykułu

Hochschild cohomology groups of certain algebras of analytic functions with coefficients in one-dimensional bimodules

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EN
Abstrakty
EN
We compute the algebraic and continuous Hochschild cohomology groups of certain Fréchet algebras of analytic functions on a domain U in $ℂ^n$ with coefficients in one-dimensional bimodules. Among the algebras considered, we focus on A=A(U). For this algebra, our results apply if U is smoothly bounded and strictly pseudoconvex, or if U is a product domain.
Słowa kluczowe
Czasopismo
Rocznik
Tom
137
Numer
1
Strony
1-31
Opis fizyczny
Daty
wydano
1999
otrzymano
1997-02-26
poprawiono
1999-08-13
Twórcy
autor
Bibliografia
  • [1] W. G. Bade, H. G. Dales and Z. A. Lykova, Algebraic and strong splittings of extensions of Banach algebras, Mem. Amer. Math. Soc. 656 (1999).
  • [2] A. Browder, Introduction to Function Algebras, W. A. Benjamin, New York, 1969.
  • [3] H. Cartan and S. Eilenberg, Homological Algebra, Princeton Univ. Press, Princeton, 1956.
  • [4] M. Crownover, One-dimensional point derivation spaces in Banach algebras, Studia Math. 35 (1970), 249-259.
  • [5] J. Eschmeier and M. Putinar, Spectral Decompositions and Analytic Sheaves, London Math. Soc. Monogr. (N.S.) 10, Oxford Univ. Press, New York, 1996.
  • [6] J. F. Feinstein, Point derivations and prime ideals in R(X), Studia Math. 98 (1991), 235-246.
  • [7] A. Ya. Helemskiĭ, The Homology of Banach and Topological Algebras, Kluwer, Dordrecht, 1989 (Russian original: Moscow Univ. Press, 1986).
  • [8] A. Ya. Helemskiĭ, Homological dimension of Banach algebras of analytic functions, Mat. Sb. 83 (1970), 222-233 (= Math. USSR-Sb. 12 (1970), 221-233).
  • [9] A. Ya. Helemskiĭ, Homological methods in the holomorphic calculus of several operators in Banach space after Taylor, Uspekhi Mat. Nauk 36 (1981), 127-172 (= Russian Math. Surveys 36 (1981), no. 1).
  • [10] A. Ya. Helemskiĭ, Flat Banach modules and amenable algebras, Trudy Moskov. Mat. Obshch. 47 (1984), 179-218 (in Russian).
  • [11] G. M. Henkin, Approximation of functions in pseudoconvex domains and the theorem of Z. L. Leibenzon, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 19 (1971), 37-42 (in Russian).
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  • [14] B. E. Johnson, Cohomology in Banach algebras, Mem. Amer. Math. Soc. 127 (1972).
  • [15] L. Kaup and B. Kaup, Holomorphic Functions of Several Variables, de Gruyter, Berlin, 1983.
  • [16] L. I. Pugach, Projective and flat ideals of function algebras and their connection with analytic structure, Mat. Zametki 31 (1982), 223-229 (in Russian).
  • [17] L. I. Pugach and M. C. White, Homology and cohomology of commutative Banach algebras and analytic polydiscs, Glasgow Math. J., 1999, to appear.
  • [18] R. M. Range, Holomorphic Functions and Integral Representations in Several Complex Variables, Grad. Texts in Math. 108, Springer, New York, 1986.
  • [19] T. T. Read, The powers of a maximal ideal in a Banach algebra and analytic structure, Trans. Amer. Math. Soc. 161 (1971), 235-248.
  • [20] J. L. Taylor, Homology and cohomology for topological algebras, Adv. Math. 9 (1972), 137-182.
  • [21] J. L. Taylor, A general framework for a multi-operator functional calculus, ibid., 183-252.
  • [22] F. Treves, Topological Vector Spaces, Distributions and Kernels, Academic Press, New York, 1967.
  • [23] C. A. Weibel, An Introduction to Homological Algebra, Cambridge Stud. Adv. Math. 38, Cambridge Univ. Press, 1994.
  • [24] M. Wodzicki, Resolution of the cohomology comparison problem for amenable Banach algebras, Invent. Math. 106 (1991), 541-547.
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Bibliografia
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bwmeta1.element.bwnjournal-article-smv137i1p1bwm
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