Integer-valued characteristics of solutions of the~noncommutative
Teoretičeskaâ i matematičeskaâ fizika, Tome 178 (2014) no. 3, pp. 307-321
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Any finite-energy solution of a noncommutative sigma model has three nonnegative integer-valued characteristics: the normalized energy $e(\Phi)$, canonical rank $r(\Phi)$, and minimum uniton number $u(\Phi)$. We prove that $r(\Phi)\ge u(\Phi)$ and $e(\Phi)\ge u(\Phi)(u(\Phi)+1)/2$. Given any numbers $e,r,u\in\mathbb N$ that satisfy the slightly stronger inequalities $r\ge u$ and $e\ge r+u(u-1)/2$, we construct a finite-energy solution $\Phi$ with $e(\Phi)=e$, $r(\Phi)=r$, and $u(\Phi)=u$.
Keywords:
noncommutative sigma model, uniton factorization.
@article{TMF_2014_178_3_a0,
author = {A. V. Domrina},
title = {Integer-valued characteristics of solutions of the~noncommutative},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {307--321},
publisher = {mathdoc},
volume = {178},
number = {3},
year = {2014},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2014_178_3_a0/}
}
A. V. Domrina. Integer-valued characteristics of solutions of the~noncommutative. Teoretičeskaâ i matematičeskaâ fizika, Tome 178 (2014) no. 3, pp. 307-321. http://geodesic.mathdoc.fr/item/TMF_2014_178_3_a0/