Invariants of Lie Algebras with Fixed Structure of Nilradicals

Abstract

An algebraic algorithm is developed for computation of invariants ('generalized Casimir operators') of general Lie algebras over the real or complex number field. Its main tools are the Cartan's method of moving frames and the knowledge of the group of inner automorphisms of each Lie algebra. Unlike the first application of the algorithm in [J. Phys. A: Math. Gen., 2006, V.39, 5749; math-ph/0602046], which deals with low-dimensional Lie algebras, here the effectiveness of the algorithm is demonstrated by its application to computation of invariants of solvable Lie algebras of general dimension $n<\infty$ restricted only by a required structure of the nilradical. Specifically, invariants are calculated here for families of real/complex solvable Lie algebras. These families contain, with only a few exceptions, all the solvable Lie algebras of specific dimensions, for whom the invariants are found in the literature.

LaTeX2e, 19 pages

References in corpus (2)

• A class of solvable Lie algebras and their Casimir Invariants
• Application of the Gel'fand Matrix Method to the Missing Label Problem in Classical Kinematical Lie Algebras

Cited by in corpus (5)

• All solvable extensions of a class of nilpotent Lie algebras of dimension n and degree of nilpotency n-1
• Internal labelling operators and contractions of Lie algebras
• Virtual copies of semisimple Lie algebras in enveloping algebras of semidirect products and Casimir operators
• Invariants of Triangular Lie Algebras
• Casimir operators induced by Maurer-Cartan equations