Geodesic
Absence of solutions to the $\sigma$-commutation problem $(\sigma\ne 0$, $\pm 1)$ for Toeplitz and Hankel matrices in a special class
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXVI, Tome 524 (2023), pp. 125-132 
V. N. Chugunov. Absence of solutions to the $\sigma$-commutation problem $(\sigma\ne 0$, $\pm 1)$ for Toeplitz and Hankel matrices in a special class. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXVI, Tome 524 (2023), pp. 125-132. http://geodesic.mathdoc.fr/item/ZNSL_2023_524_a9/
@article{ZNSL_2023_524_a9,
     author = {V. N. Chugunov},
     title = {Absence of solutions to the $\sigma$-commutation problem $(\sigma\ne 0$, $\pm 1)$ for {Toeplitz} and {Hankel} matrices in a special class},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {125--132},
     year = {2023},
     volume = {524},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2023_524_a9/}
}
TY  - JOUR
AU  - V. N. Chugunov
TI  - Absence of solutions to the $\sigma$-commutation problem $(\sigma\ne 0$, $\pm 1)$ for Toeplitz and Hankel matrices in a special class
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2023
SP  - 125
EP  - 132
VL  - 524
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2023_524_a9/
LA  - ru
ID  - ZNSL_2023_524_a9
ER  - 
%0 Journal Article
%A V. N. Chugunov
%T Absence of solutions to the $\sigma$-commutation problem $(\sigma\ne 0$, $\pm 1)$ for Toeplitz and Hankel matrices in a special class
%J Zapiski Nauchnykh Seminarov POMI
%D 2023
%P 125-132
%V 524
%U http://geodesic.mathdoc.fr/item/ZNSL_2023_524_a9/
%G ru
%F ZNSL_2023_524_a9

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

It is established that the $\sigma$-commutation problem for Toeplitz and Hankel matrices has no solutions in a particular subset.

[1] A. E. Guterman, O. V. Markova, V. Mehrmann, “Length realizability for pairs of quasi-commuting matrices”, Linear Algebra Appl., 568 (2019), 135–154 | DOI | MR | Zbl

[2] C. Kassel, Quantum Groups, Grad. Texts in Math., 155, Springer-Verlag, New York, 1995 | DOI | MR | Zbl

[3] Yu. I. Manin, Quantum Groups and Non-Sommutative Geometry, CRM, Montréal, 1988 | MR

[4] N. Chriss, V. Ginzburg, Representation Theory and Complex Geometry, Birkhäuser, Boston–Basel–Berlin, 1997 | MR | Zbl

[5] V. N. Chugunov, “O nekotorykh mnozhestvakh par $\sigma$-kommutiruyuschikh ($\sigma \ne 0, \pm 1$) teplitsevoi i gankelevoi matrits”, Zap. nauchn. semin. POMI, 482 (2019), 288–294

[6] V. N. Chugunov, Kh. D. Ikramov, “Ob odnom chastnom reshenii zadachi o $\sigma$-kommutirovanii ($\sigma\ne 0, \pm 1$) teplitsevoi i gankelevoi matrits”, Zh. vychisl. matem. matem. fiz., 63:11 (2023), 1817–1828

[7] V. I. Gelfgat, “Usloviya kommutirovaniya teplitsevykh matrits”, Zh. vychisl. matem. matem. fiz., 38:1 (1998), 11–14 | MR | Zbl