Commutative matrix subalgebras and length function

A. E. Guterman; O. V. Markova

doi:10.1016/j.laa.2008.07.010

Commutative matrix subalgebras and length function

A. E. Guterman, O. V. Markova

Research output: Contribution to journal › Article › peer-review

27 Scopus citations

Abstract

It is proved that if the length of a commutative matrix subalgebra is maximal then this subalgebra is maximal under inclusion. The examples are given showing that the converse does not hold. To establish this result, we prove several fundamental properties of the length function.

Original language	English
Pages (from-to)	1790-1805
Number of pages	16
Journal	Linear Algebra and Its Applications
Volume	430
Issue number	7
DOIs	https://doi.org/10.1016/j.laa.2008.07.010
State	Published - 1 Apr 2009
Externally published	Yes

Bibliographical note

Funding Information:
This work is partially supported by the grants: RFBR 08-01-00693a, MK-2718.2007.1 and NSh-1983.2008.1. ∗ Corresponding author. E-mail address: guterman@list.ru (A.E. Guterman).

Keywords

Commutative matrix algebras
Finite-dimensional algebras
Matrix length

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10.1016/j.laa.2008.07.010

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keywords = "Commutative matrix algebras, Finite-dimensional algebras, Matrix length",

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note = "Funding Information: This work is partially supported by the grants: RFBR 08-01-00693a, MK-2718.2007.1 and NSh-1983.2008.1. ∗ Corresponding author. E-mail address: guterman@list.ru (A.E. Guterman).",

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AU - Markova, O. V.

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AB - It is proved that if the length of a commutative matrix subalgebra is maximal then this subalgebra is maximal under inclusion. The examples are given showing that the converse does not hold. To establish this result, we prove several fundamental properties of the length function.

KW - Commutative matrix algebras

KW - Finite-dimensional algebras

KW - Matrix length

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Commutative matrix subalgebras and length function

Abstract

Bibliographical note

Keywords

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