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Fundam. Prikl. Mat., 2007, Volume 13, Issue 4, Pages 165–197 (Mi fpm1069)  

This article is cited in 12 scientific papers (total in 12 papers)

Length computation of matrix subalgebras of special type

O. V. Markova

M. V. Lomonosov Moscow State University

Abstract: Let $\mathbb F$ be a field and let $\mathcal A$ be a finite-dimensional $\mathbb F$-algebra. We define the length of a finite generating set of this algebra as the smallest number $k$ such that words of length not greater than $k$ generate $\mathcal A$ as a vector space, and the length of the algebra is the maximum of the lengths of its generating sets. In this article, we give a series of examples of length computation for matrix subalgebras. In particular, we evaluate the lengths of certain upper triangular matrix subalgebras and their direct sums, and the lengths of classical commutative matrix subalgebras. The connection between the length of an algebra and the lengths of its subalgebras is also studied.

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English version:
Journal of Mathematical Sciences (New York), 2008, 155:6, 908–931

Bibliographic databases:

UDC: 512.643

Citation: O. V. Markova, “Length computation of matrix subalgebras of special type”, Fundam. Prikl. Mat., 13:4 (2007), 165–197; J. Math. Sci., 155:6 (2008), 908–931

Citation in format AMSBIB
\by O.~V.~Markova
\paper Length computation of matrix subalgebras of special type
\jour Fundam. Prikl. Mat.
\yr 2007
\vol 13
\issue 4
\pages 165--197
\jour J. Math. Sci.
\yr 2008
\vol 155
\issue 6
\pages 908--931

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    This publication is cited in the following articles:
    1. Guterman A.E., Markova O.V., “Commutative matrix subalgebras and length function”, Linear Algebra Appl., 430:7 (2009), 1790–1805  crossref  mathscinet  zmath  isi  elib
    2. O. V. Markova, “Upper bound for the length of commutative algebras”, Sb. Math., 200:12 (2009), 1767–1787  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. O. V. Markova, “On Some Properties of the Length Function”, Math. Notes, 87:1 (2010), 71–78  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. O. V. Markova, “Classification of matrix subalgebras of length 1”, J. Math. Sci., 185:3 (2012), 458–472  mathnet  crossref
    5. O. V. Markova, “The length function and matrix algebras”, J. Math. Sci., 193:5 (2013), 687–768  mathnet  crossref
    6. O. V. Markova, “Description of algebras of length $1$”, Moscow University Mathematics Bulletin, 68:1 (2013), 74–76  mathnet  crossref  mathscinet
    7. O. V. Markova, “On the Relationship between the Length of an Algebra and the Index of Nilpotency of Its Jacobson Radical”, Math. Notes, 94:5 (2013), 636–641  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    8. A. E. Guterman, O. V. Markova, “The realizability problem for values of the length function for quasi-commuting matrix pairs”, J. Math. Sci. (N. Y.), 216:6 (2016), 761–769  mathnet  crossref  mathscinet
    9. N. A. Kolegov, O. V. Markova, “Sistemy porozhdayuschikh matrichnykh algebr intsidentnosti nad konechnymi polyami”, Chislennye metody i voprosy organizatsii vychislenii. XXXI, Zap. nauchn. sem. POMI, 472, POMI, SPb., 2018, 120–144  mathnet
    10. Guterman A. Laffey T. Markova O. Smigoc H., “A Resolution of Paz'S Conjecture in the Presence of a Nonderogatory Matrix”, Linear Alg. Appl., 543 (2018), 234–250  crossref  mathscinet  zmath  isi  scopus
    11. Guterman A.E., Markova V O., Mehrmann V., “Length Realizability For Pairs of Quasi-Commuting Matrices”, Linear Alg. Appl., 568 (2019), 135–154  crossref  mathscinet  zmath  isi  scopus
    12. N. A. Kolegov, O. V. Markova, “Dlina matrichnykh algebr intsidentnosti nad malenkimi konechnymi polyami”, Chislennye metody i voprosy organizatsii vychislenii. XXXIV, Zap. nauchn. sem. POMI, 504, POMI, SPb., 2021, 102–135  mathnet
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