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Tr. Mat. Inst. Steklova, 2017, Volume 298, Pages 112–126 (Mi tm3807)  

On the Dimension of Solution Spaces of a Noncommutative Sigma Model in the Case of Uniton Number 2

A. V. Domrinaa, A. V. Domrinb

a Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119991 Russia
b Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119991 Russia

Abstract: We show that the complex dimension of the set of solutions of the noncommutative $U(1)$ sigma model that are finite-dimensional perturbations of the identity operator and have canonical rank $r$ and minimal uniton number $2$ is equal to $r$. We give explicit formulas for all such solutions.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00117
16-52-12012
17-01-00592
This work was supported by the Russian Foundation for Basic Research, project nos. 16-01-00117, 16-52-12012, and 17-01-00592.


DOI: https://doi.org/10.1134/S0371968517030086

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English version:
Proceedings of the Steklov Institute of Mathematics, 2017, 298, 104–117

Bibliographic databases:

Document Type: Article
UDC: 517.986.9
Received: February 16, 2017

Citation: A. V. Domrina, A. V. Domrin, “On the Dimension of Solution Spaces of a Noncommutative Sigma Model in the Case of Uniton Number 2”, Complex analysis and its applications, Collected papers. On the occasion of the centenary of the birth of Boris Vladimirovich Shabat, 85th anniversary of the birth of Anatoliy Georgievich Vitushkin, and 85th anniversary of the birth of Andrei Aleksandrovich Gonchar, Tr. Mat. Inst. Steklova, 298, MAIK Nauka/Interperiodica, Moscow, 2017, 112–126; Proc. Steklov Inst. Math., 298 (2017), 104–117

Citation in format AMSBIB
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\paper On the Dimension of Solution Spaces of a Noncommutative Sigma Model in the Case of Uniton Number 2
\inbook Complex analysis and its applications
\bookinfo Collected papers. On the occasion of the centenary of the birth of Boris Vladimirovich Shabat, 85th anniversary of the birth of Anatoliy Georgievich Vitushkin, and 85th anniversary of the birth of Andrei Aleksandrovich Gonchar
\serial Tr. Mat. Inst. Steklova
\yr 2017
\vol 298
\pages 112--126
\publ MAIK Nauka/Interperiodica
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