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The formal de Rham complex

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Abstract

We propose a formal construction generalizing the classic de Rham complex to a wide class of models in mathematical physics and analysis. The presentation is divided into a sequence of definitions and elementary, easily verified statements; proofs are therefore given only in the key case. Linear operations are everywhere performed over a fixed number field \(\mathbb{F} = \mathbb{R},\mathbb{C}\). All linear spaces, algebras, and modules, although not stipulated explicitly, are by definition or by construction endowed with natural locally convex topologies, and their morphisms are continuous.

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Authors and Affiliations

  1. Steklov Mathematical Institute, RAS, Moscow, Russia

    V. V. Zharinov

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  1. V. V. Zharinov
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Correspondence to V. V. Zharinov.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 174, No. 2, pp. 256–271, February, 2013.

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Zharinov, V.V. The formal de Rham complex. Theor Math Phys 174, 220–235 (2013). https://doi.org/10.1007/s11232-013-0019-z

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