@article{ZNSL_2019_482_a4,
author = {A. E. Guterman and D. K. Kudryavtsev and O. V. Markova},
title = {Length of a direct sum of nonassociative algebras},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {73--86},
year = {2019},
volume = {482},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2019_482_a4/}
}
A. E. Guterman; D. K. Kudryavtsev; O. V. Markova. Length of a direct sum of nonassociative algebras. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXII, Tome 482 (2019), pp. 73-86. http://geodesic.mathdoc.fr/item/ZNSL_2019_482_a4/
[1] Yu. A. Alpin, Kh. D. Ikramov, “Ob unitarnom podobii matrichnykh semeistv”, Matem. zametki, 74:6 (2003), 815–826 | DOI | Zbl
[2] Yu. A. Al'pin, Kh. D. Ikramov, “Reducibility theorems for pairs of matrices as rational criteria”, Linear Algebra Appl., 313 (2000), 155–161 | DOI | MR | Zbl
[3] V. Futorny, R. A. Horn, V. V. Sergeichuk, “Specht's criterion for systems of linear mappings”, Linear Algebra Appl., 519 (2017), 278–295 | DOI | MR | Zbl
[4] A. E. Guterman, D. K. Kudryavtsev, “Dlina algebr kvaternionov i oktonionov”, Zap. nauchn. semin. POMI, 453, 2016, 22–32
[5] A. E. Guterman, D. K. Kudryavtsev, “Upper bounds for the length of non-associative algebras”, J. Algebra (to appear) ; February, 2019, arXiv: 1902.08389 [math.CO] | MR
[6] A. Guterman, T. Laffey, O. Markova, H. Šmigoc, “A resolution of Paz's conjecture in the presence of a nonderogatory matrix”, Linear Algebra Appl., 543 (2018), 234–250 | DOI | MR | Zbl
[7] A. E. Guterman, O. V. Markova, “Commutative matrix subalgebras and length function”, Linear Algebra Appl., 430 (2009), 1790–1805 | DOI | MR | Zbl
[8] A. E. Guterman, O. V. Markova, “Dlina gruppovykh algebr grupp nebolshogo razmera”, Zap. nauchn. semin. POMI, 472, 2018, 76–87
[9] A. Guterman, O. Markova, V. Mehrmann, “Length realizability for pairs of quasi-commuting matrices”, Linear Algebra Appl., 568 (2019), 135–154 | DOI | MR | Zbl
[10] N. A. Kolegov, O. V. Markova, “Sistemy porozhdayuschikh matrichnykh algebr intsidentnosti nad konechnymi polyami”, Zap. nauchn. semin. POMI, 472, 2018, 120–144
[11] O. V. Markova, “Verkhnyaya otsenka dliny kommutativnykh algebr”, Matem. sb., 200:12 (2009), 41–62 | DOI | Zbl
[12] O. V. Markova, “Funktsiya dliny i matrichnye algebry”, Fund. prikl. mat., 17:6 (2012), 65–173
[13] O. V. Markova, “O dline algebry verkhnetreugolnykh matrits”, Uspekhi matem. nauk, 60:3 (2005), 177–178 | DOI | MR | Zbl
[14] C. J. Pappacena, “An upper bound for the length of a finite-dimensional algebra”, J. Algebra, 197 (1997), 535–545 | DOI | MR | Zbl
[15] A. Paz, “An application of the Cayley–Hamilton theorem to matrix polynomials in several variables”, Linear Multilinear Algebra, 15 (1984), 161–170 | DOI | MR | Zbl
[16] Ya. Shitov, “An improved bound for the length of matrix algebras”, Algebra Number Theory, 13 (2019), 1501–1507 | DOI | MR | Zbl
[17] A. J. M. Spencer, R. S. Rivlin, “The theory of matrix polynomials and its applications to the mechanics of isotropic continua”, Arch. Ration. Mech. Anal., 2 (1959), 309–336 | DOI | MR | Zbl
[18] A. J. M. Spencer, R. S. Rivlin, “Further results in the theory of matrix polynomials”, Arch. Ration. Mech. Anal., 4 (1960), 214–230 | DOI | MR | Zbl