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TMF, 2013, Volume 174, Number 2, Pages 256–271 (Mi tmf8402)  

This article is cited in 5 scientific papers (total in 5 papers)

The formal de Rham complex

V. V. Zharinov

Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, Russia

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.

Keywords: de Rham complex, multiplicator, derivation, exterior algebra, boundary operator, exterior differential, complex associated with an algebra, grading

Funding Agency Grant Number
Russian Foundation for Basic Research 10-01-00178
Ministry of Education and Science of the Russian Federation НШ-7675.2010.1


DOI: https://doi.org/10.4213/tmf8402

Full text: PDF file (461 kB)
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English version:
Theoretical and Mathematical Physics, 2013, 174:2, 220–235

Bibliographic databases:

Received: 20.08.2012

Citation: V. V. Zharinov, “The formal de Rham complex”, TMF, 174:2 (2013), 256–271; Theoret. and Math. Phys., 174:2 (2013), 220–235

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. V. Zharinov, “Algebraic aspects of gauge theories”, Theoret. and Math. Phys., 180:2 (2014), 942–957  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    2. V. V. Zharinov, “Conservation laws, differential identities, and constraints of partial differential equations”, Theoret. and Math. Phys., 185:2 (2015), 1557–1581  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. V. V. Zharinov, “Lie–Poisson structures over differential algebras”, Theoret. and Math. Phys., 192:3 (2017), 1337–1349  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    4. V. V. Zharinov, “Analysis in algebras and modules”, Proc. Steklov Inst. Math., 301 (2018), 98–108  mathnet  crossref  crossref  isi  elib  elib
    5. V. V. Zharinov, “Analysis in differential algebras and modules”, Theoret. and Math. Phys., 196:1 (2018), 939–956  mathnet  crossref  crossref  adsnasa  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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