Correction to: A classification of nilpotent compatible Lie algebras (Rendiconti del Circolo Matematico di Palermo Series 2, (2025), 74, 1, (70), 10.1007/s12215-024-01126-z)

Abstract

We have made a computational mistake when calculating the orbits of some cocycles in Section 4.4 of the original paper. This makes it so that three families of orbits (and thus three compatible Lie algebra isomorphism families), which previously depended on the field structure, now do not, and now depend on one less parameter. Thus, the classification is independent of the base field (as long as the characteristic is not 2). Section4.4:IntheclassificationoftheextensionsofNCL3,2 The computation of the last orbit (page 23) should read (Figure presented.) and be followed by (Figure presented.) At the end of the same page, the discussion regarding the parameter ß in O([1+ß5]) should be disregarded, and the discussion regarding O([1+ß4]) and O([1+ß5]) should have the parameter ß replaced by 1. Finally, the list of algebras that are obtained from NCL3,2 should read (Figure presented.) Section4.4:IntheclassificationoftheextensionsofNCL3,3 This whole subsection should now read (Figure presented.) Section4.4:IntheclassificationoftheextensionsofNCL3,4 Equation (12) on page 25 should now read (Figure presented.) At the bottom of the same page, it should read (Figure presented.) (c) 2025 Elsevier B.V., All rights reserved.