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.

arXiv commentLaTeX2e, 19 pages

References in corpus (8)

• Bound states in a 2D short range potential induced by spin-orbit interaction
• A class of solvable Lie algebras and their Casimir Invariants
• Computation of Invariants of Lie Algebras by Means of Moving Frames
• Solvable Lie algebras with triangular nilradicals
• Solvable Lie algebras with naturally graded nilradicals and their invariants
• Ballistic spin currents in mesoscopic metal/In(Ga)As/metal junctions
• Invariants of the nilpotent and solvable triangular Lie algebras
• Application of the Gel'fand Matrix Method to the Missing Label Problem in Classical Kinematical Lie Algebras

Cited by in corpus (11)

• Computation of Invariants of Lie Algebras by Means of Moving Frames
• Can solvable extensions of a nilpotent subalgebra be useful in the classification of solvable algebras with the given nilradical?
• All solvable extensions of a class of nilpotent Lie algebras of dimension n and degree of nilpotency n-1
• Invariants of solvable Lie algebras with triangular nilradicals and diagonal nilindependent elements
• 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
• Invariants of triangular Lie algebras with one nilindependent diagonal element
• Generalized conformal pseudo-Galilean algebras and their Casimir operators
• Invariants of Lie algebras via moving frames
• Casimir operators induced by Maurer-Cartan equations