Abstract
For a natural number m, a Lie algebra L over a field k is said to be of breadth type if the co-dimension of the centralizer of every non-central element is m. In this article, we classify finite dimensional nilpotent Lie algebras of breadth type
over
of odd characteristic up to isomorphism. We also give a partial classification of the same over finite fields of even characteristic,
and
. We also discuss 2-step nilpotent Camina Lie algebras.
Disclosure Statement
There is no conflict of interest for this article.
Acknowledgments
We thank Pradeep Kumar Rai for his interest in this problem. We also thank the anonymous referee for his/her valuable comments.