Invariants of the nilpotent and solvable triangular Lie algebras

Details Invariants of the nilpotent and solvable triangular Lie algebras Invariants of the nilpotent and solvable triangular Lie algebras

2007-09-19

arxiv.org/abs/0709.3116v1

J. Phys. A: Math. Gen., 34, No 42, (2001) 9085-9099

Physics

Mathematical Physics

Scientific paper

10.1088/0305-4470/34/42/323

Invariants of the coadjoint representation of two classes of Lie algebras are calculated. The first class consists of the nilpotent Lie algebras $T(M)$, isomorphic to the algebras of upper triangular $M\times M$ matrices. The Lie algebra $T(M)$ is shown to have $[M/2]$ functionally independent invariants. They can all be chosen to be polynomials and they are presented explicitly. The second class consists of the solvable Lie algebras $L(M,f)$ with $T(M)$ as their nilradical and $f$ additional linearly nilindependent elements. Some general results on the invariants of $L(M,f)$ are given and the cases M=4 for all $f$ and $f=1$, or $f=M-1$ for all $M$ are treated in detail.

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