Geodesic
The formal de Rham complex
Teoretičeskaâ i matematičeskaâ fizika, Tome 174 (2013) no. 2, pp. 256-271 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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},
     year = {2013},
     volume = {174},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2013_174_2_a5/}
}
TY  - JOUR
AU  - V. V. Zharinov
TI  - The formal de Rham complex
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2013
SP  - 256
EP  - 271
VL  - 174
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2013_174_2_a5/
LA  - ru
ID  - TMF_2013_174_2_a5
ER  - 
%0 Journal Article
%A V. V. Zharinov
%T The formal de Rham complex
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2013
%P 256-271
%V 174
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2013_174_2_a5/
%G ru
%F 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/

[1] S. Maklein, Gomologiya, Mir, M., 1966 | MR | Zbl

[2] V. V. Zharinov, Integral Transforms Spec. Funct., 6:1–4 (1998), 347–356 | DOI | MR | Zbl

[3] S. Khelgason, Differentsialnaya geometriya, gruppy Li i simmetricheskie prostranstva, Faktorial Press, M., 2005 | MR | Zbl

[4] J. Madore, An Introduction to Noncommutative Differential Geometry and its Physical Applications, London Mathematical Society Lecture Note Series, 206, Cambridge Univ. Press, Cambridge, 1995 | MR | Zbl

[5] S. Sakai, $C^*$-Algebras and $W^*$-Algebras, Springer, Berlin, 1971 | MR | Zbl

[6] B. A. Dubrovin, S. P. Novikov, A. T. Fomenko, Sovremennaya geometriya. Metody i prilozheniya, v. 3, Teoriya gomologii, Nauka, M., 1984 | MR | Zbl

[7] A. Kartan, Differentsialnoe ischislenie. Differentsialnye formy, Mir, M., 1971 | MR | Zbl

[8] L. Schwartz, Théorie des distributions. Tome I, Actualites scientifiques et industrielles, 1091, Hermann Cie., Paris, 1950 ; Tome II, 1121, 1951 | MR | Zbl | MR | Zbl

[9] V. S. Vladimirov, Obobschennye funktsii v matematicheskoi fizike, Nauka, M., 1976 | MR | Zbl

[10] I. M. Gelfand, G. E. Shilov, Obobschennye funktsii i deistviya nad nimi, Fizmatlit, M., 1959 | MR | Zbl

[11] R. Bott, L. V. Tu, Differentsialnye formy v algebraicheskoi topologii, Nauka, M., 1989 | MR

[12] V. V. Zharinov, TMF, 170:3 (2012), 323–334 | DOI | DOI | Zbl

[13] V. V. Zharinov, TMF, 172:1 (2012), 3–8 | DOI | Zbl