On orthogonal and special orthogonal invariants of a single matrix of small order

Details On orthogonal and special orthogonal invariants of a single matrix of small order On orthogonal and special orthogonal invariants of a single matrix of small order

2007-09-03

arxiv.org/abs/0709.0146v2

Linear and Multilinear Algebra 57 (2009), No. 4, 345-354.

Mathematics

Commutative Algebra

13 pages, 3 tables, no figures. Four misprints in Section 2 corrected. The paper will appear in "Linear and Multilinear Algebr

Scientific paper

We study the structure of the algebra of polynomial invariants for the usual conjugation action of the complex special, SO_n, and general, O_n, orthogonal group on the space of traceless n by n complex matrices. (Note that these two algebras coincide if n is odd.) Minimal generating sets of these algebras are known for n less than 5. We construct one for n=5. We also construct a Hironaka decomposition in the case n=3 and a new (more economical) such decomposition for n=4. A simple presentation (with just one syzygy) is obtained for the algebra in the case n=3.

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