Geodesic
Description of solutions with the uniton number $3$ in the case of one eigenvalue: Counterexample to the dimension conjecture
Teoretičeskaâ i matematičeskaâ fizika, Tome 201 (2019) no. 1, pp. 3-16
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We explicitly describe solutions of the noncommutative unitary $U(1)$ sigma model that represent finite-dimensional perturbations of the identity operator and have only one eigenvalue and the minimum uniton number $3$. We also show that the solution set $M(e,r,u)$ of energy $e$ and canonical rank $r$ with the minimum uniton number $u=3$ has a complex dimension greater than $r$ for $e=4n-1$ and $r=n+1$, where $n\ge3$. This disproves the dimension conjecture that holds in the case $u\in\{1,2\}$.
Keywords: noncommutative sigma model, uniton theory. 
@article{TMF_2019_201_1_a0,
     author = {A. V. Domrina},
     title = {Description of solutions with the~uniton number $3$ in the~case of one eigenvalue: {Counterexample} to the~dimension conjecture},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {3--16},
     year = {2019},
     volume = {201},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2019_201_1_a0/}
}
TY  - JOUR
AU  - A. V. Domrina
TI  - Description of solutions with the uniton number $3$ in the case of one eigenvalue: Counterexample to the dimension conjecture
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2019
SP  - 3
EP  - 16
VL  - 201
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2019_201_1_a0/
LA  - ru
ID  - TMF_2019_201_1_a0
ER  - 
%0 Journal Article
%A A. V. Domrina
%T Description of solutions with the uniton number $3$ in the case of one eigenvalue: Counterexample to the dimension conjecture
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2019
%P 3-16
%V 201
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2019_201_1_a0/
%G ru
%F TMF_2019_201_1_a0
A. V. Domrina. Description of solutions with the uniton number $3$ in the case of one eigenvalue: Counterexample to the dimension conjecture. Teoretičeskaâ i matematičeskaâ fizika, Tome 201 (2019) no. 1, pp. 3-16. http://geodesic.mathdoc.fr/item/TMF_2019_201_1_a0/

[1] L. Khermander, Analiz lineinykh differentsialnykh operatorov s chastnymi proizvodnymi, v. 3, Psevdodifferentsialnye operatory, Mir, M., 1989 | MR | Zbl

[2] A. V. Domrin, “Nekommutativnye unitony”, TMF, 154:2, 220–239 | DOI | DOI | MR | Zbl

[3] A. V. Domrin, “Prostranstva modulei reshenii nekommutativnoi sigma-modeli”, TMF, 156:3, 307–327 | DOI | DOI | MR | Zbl

[4] A. V. Domrina, “Petlevye podnyatiya v nekommutativnoi sigma-modeli”, Tr. MIAN, 279 (2012), 72–80 | DOI | MR

[5] A. V. Domrina, “Tselochislennye kharakteristiki reshenii nekommutativnoi sigma-modeli”, TMF, 178:3, 307–321 | DOI | DOI | MR | Zbl

[6] A. V. Domrina, A. V. Domrin, “O razmernosti prostranstv reshenii nekommutativnoi sigma-modeli v sluchae unitonnogo chisla $2$”, Tr. MIAN, 298 (2017), 112–126 | DOI | DOI