Abstract
If an analytic algebra
is an analytic tensor product A=B⊗C, then we have a corresponding decomposition of the module of differentials
\(\Omega ^1 (A) = \Omega ^{1,0} (B,C) \oplus \Omega ^{0,1} (B,C)\). In this paper we study the converse problem: Given a decomposition\(\Omega ^1 (A) = \Omega ' \oplus \Omega ''\), can it be obtained from an analytic tensor product? A necessary and sufficient condition is given by the FROBENIUS theorem in the classical case (A regular). We show that the FROBENIUS theorem holds for algebras with contractions compatible with the given decomposition too.
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Herrn F. Sommer zum 60. Geburtstag.
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Reiffen, HJ. Zum Frobenius Theorem auf komplexen Räumen. Manuscripta Math 9, 229–243 (1973). https://doi.org/10.1007/BF01303854
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DOI: https://doi.org/10.1007/BF01303854