The~formal de~Rham complex
Teoretičeskaâ i matematičeskaâ fizika, Tome 174 (2013) no. 2, pp. 256-271
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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.
Keywords:
de Rham complex, multiplicator, derivation, exterior algebra, boundary operator, exterior differential, complex associated with an algebra, grading.
@article{TMF_2013_174_2_a5,
author = {V. V. Zharinov},
title = {The~formal {de~Rham} complex},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {256--271},
publisher = {mathdoc},
volume = {174},
number = {2},
year = {2013},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2013_174_2_a5/}
}
V. V. Zharinov. The~formal de~Rham complex. Teoretičeskaâ i matematičeskaâ fizika, Tome 174 (2013) no. 2, pp. 256-271. http://geodesic.mathdoc.fr/item/TMF_2013_174_2_a5/