Repository: DepositOnce â€“ institutional repository for research data and publications of TU Berlin https://depositonce.tu-berlin.de
TY - RPRT
AU - Guterman, Alexander E.
AU - Markova, Olga V.
AU - Mehrmann, Volker
PY - 2015
TI - Lengths of quasi-commutative pairs of matrices
DO - 10.14279/depositonce-14623
UR - http://dx.doi.org/10.14279/depositonce-14623
PB - Technische UniversitÃ¤t Berlin
LA - en
AB - 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.
KW - finite-dimensional algebras
KW - lengths of sets and algebras
KW - quasi-commuting matrices
ER -