SOLVABLE LIE-ALGEBRAS OF DIMENSION LESS-THAN-OR-EQUAL-TO 4 OVER PERFECT FIELDS

The solvable Lie algebras of dimension not greater than four over a perfect field of reference are described in terms of their nilpotent frame, counted over finite fields of q elements, and classified over the real and complex number fields. The number dq,n of nonisomorphic solvable Lie algebras of dimension n over Fq roughly speaking grows as a polynomial in n with qn-2 as highest term. But there are smaller additional terms depending on the residue class of q modulo (n-1)! if n≤4. © 1990.