COMPUTING THE LAW OF A FAMILY OF SOLVABLE LIE ALGEBRAS

Abstract

This paper shows an algorithm which computes the law of the Lie algebra associated with the complex Lie group of n × n upper-triangular matrices with exponential elements in their main diagonal. For its implementation two procedures are used, respectively, to define a basis of the Lie algebra and the nonzero brackets in its law with respect to that basis. These brackets constitute the final output of the algorithm, whose unique input is the matrix order n. Besides, its complexity is proved to be polynomial and some complementary computational data relative to its implementation are also shown.