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Main Title: Lengths of quasi-commutative pairs of matrices
Author(s): Guterman, Alexander E.
Markova, Olga V.
Mehrmann, Volker
Type: Research Paper
Abstract: In this paper we discuss some partial solutions of the length conjecture which describes the length of a generating system for matrix algebras. We consider mainly the algebras generated by two matrices which are quasi-commuting. It is shown that in this case the length function is linearly bounded. We also analyze which particular natural numbers can be realized as the lengths of certain special generating sets and prove that for commuting or product-nilpotent pairs all possible numbers are realizable, however there are non-realizable values between lower and upper bounds for the other quasi-commuting pairs. In conclusion we also present several related open problems.
Subject(s): finite-dimensional algebras
lengths of sets and algebras
quasi-commuting matrices
Issue Date: 18-Jun-2015
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 15A30 Algebraic systems of matrices
16S50 Endomorphism rings; matrix rings
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2015, 09
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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