Mathematical Journal of Okayama University volume67 issue1
2025-01 発行
Locally serially coalescent classes of Lie algebras
Honda, Masanobu
Faculty of Pharmaceutical Sciences, Niigata University of Pharmacy and Medical and Life Sciences
Sakamoto, Takanori
Department of Mathematics, University of Teacher Education Fukuoka
Publication Date
2025-01
Abstract
We assume that a basic field k has zero characteristic. We show that any Fitting class is serially coalescent for locally finite Lie algebras. We also show that any class X satisfying N ≤ X ≤ ˆGr (e.g. Ft, B, Z, Gr, lN, rN, `e(◁)ˆA, ˆe(◁)ˆA, `Gr) is locally serially coalescent for locally finite Lie algebras, and, for any locally finite Lie algebra L, the X-ser radical of L is locally nilpotent.
Keywords
Lie algebra
serial subalgebra
locally coalescent class
Comments
Mathematics Subject Classification. Primary 17B65; Secondary 17B30.
ISSN
0030-1566
NCID
AA00723502
