An algebra which is a maximal commutative subalgebra in very few algebras
Volume 147 / 2017
Colloquium Mathematicum 147 (2017), 241-246
MSC: Primary 16S50; Secondary 46H10; 47L10.
DOI: 10.4064/cm6941-6-2016
Published online: 13 January 2017
Abstract
“Very few” in the title means two. We show that a unital real or complex algebra generated by a nilpotent of order two can be a maximal abelian subalgebra only in two algebras. One of them is of dimension three and the other of dimension four.
