Analysis in Noncommutative Algebras and Modules
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematical physics and applications, Tome 306 (2019), pp. 100-111.

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In a previous paper, we developed an analysis in associative commutative algebras and in modules over them, which may be useful in problems of contemporary mathematical and theoretical physics. Here we work out similar methods in the noncommutative case.
Keywords: associative noncommutative algebra, derivation, covariant derivation, gauge transform, differential form, cohomology.
Mots-clés : module, multiplier, moduli space
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V. V. Zharinov. Analysis in Noncommutative Algebras and Modules. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematical physics and applications, Tome 306 (2019), pp. 100-111. http://geodesic.mathdoc.fr/item/TM_2019_306_a8/

[1] Connes A., “Non-commutative differential geometry”, Publ. math. Inst. hautes étud. sci., 62 (1985), 41–144 | DOI | MR | Zbl

[2] Connes A., Marcolli M., Noncommutative geometry, quantum fields and motives, AMS Colloq. Publ., 55, Amer. Math. Soc., Providence, RI, 2008 | MR | Zbl

[3] A. K. Gushchin, “$L_p$-estimates for the nontangential maximal function of the solution to a second-order elliptic equation”, Sb. Math., 207 (2016), 1384–1409 | DOI | DOI | MR | Zbl

[4] M. O. Katanaev, “Killing vector fields and a homogeneous isotropic universe”, Phys. Usp., 59:7 (2016), 689–700 | DOI | DOI

[5] M. O. Katanaev, “Cosmological models with homogeneous and isotropic spatial sections”, Theor. Math. Phys., 191:2 (2017), 661–668 | DOI | DOI | MR | MR | Zbl

[6] S. V. Kozyrev, “Ultrametricity in the theory of complex systems”, Theor. Math. Phys., 185:2 (2015), 1665–1677 | DOI | DOI | MR | Zbl

[7] Kozyrev S.V., Mironov A.A., Teretenkov A.E., Volovich I.V., “Flows in non-equilibrium quantum systems and quantum photosynthesis”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 20:4 (2017), 1750021 | DOI | MR | Zbl

[8] Madore J., An introduction to noncommutative differential geometry and its physical applications, LMS Lect. Note Ser., 257, Cambridge Univ. Press, Cambridge, 1999 | MR | Zbl

[9] N. G. Marchuk, “Demonstration representation and tensor products of Clifford algebras”, Proc. Steklov Inst. Math., 290 (2015), 143–154 | DOI | DOI | MR | Zbl

[10] A. N. Pechen and N. B. Il'in, “Existence of traps in the problem of maximizing quantum observable averages for a qubit at short times”, Proc. Steklov Inst. Math., 289 (2015), 213–220 | DOI | DOI | MR | Zbl

[11] A. G. Sergeev, “Spin geometry of Dirac and noncommutative geometry of Connes”, Proc. Steklov Inst. Math., 298 (2017), 256–293 | DOI | DOI | MR | Zbl

[12] Volovich I.V., “Cauchy–Schwarz inequality-based criteria for the non-classicality of sub-Poisson and antibunched light”, Phys. Lett. A, 380:1–2 (2016), 56–58 | DOI | MR | Zbl

[13] V. V. Zharinov, “The formal de Rham complex”, Theor. Math. Phys., 174:2 (2013), 220–235 | DOI | DOI | MR | Zbl

[14] V. V. Zharinov, “Bäcklund transformations”, Theor. Math. Phys., 189:3 (2016), 1681–1692 | DOI | DOI | MR | MR | Zbl

[15] V. V. Zharinov, “Analysis in algebras and modules”, Proc. Steklov Inst. Math., 301 (2018), 98–108 | DOI | DOI | MR | Zbl