Breadth and characteristic sequence of nilpotent Lie algebras

The notion of breadth of a nilpotent Lie algebra was introduced and used to approach problems of classification up to isomorphism in [5 Khuhirun, B., Misra, K. C., Stitzinger, E. (2015). On nilpotent Lie algebras of small breadth. J. Algebra 444:328–338.[Crossref], [Web of Science ®] , [Google Scholar]]. In the present paper, we study this invariant in terms of characteristic sequence, another invariant, introduced by Goze and Ancochea in [1 Ancochea-Bermúdez, J. M., Goze, M. (1986). Sur la classification des algèbres de Lie nilpotentes de dimension 7. C. R. Acad. Sci. Paris 302:611–613. [Google Scholar]]. This permits to complete the determination of Lie algebras of breadth 2 studied in [5 Khuhirun, B., Misra, K. C., Stitzinger, E. (2015). On nilpotent Lie algebras of small breadth. J. Algebra 444:328–338.[Crossref], [Web of Science ®] , [Google Scholar]] and to begin the work for Lie algebras with breadth greater than 2.