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Gröbner Bases for the Rings of Special Orthogonal and 2 × 2 Matrix Invariants

✍ Scribed by M Domokos; V Drensky

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
110 KB
Volume
243
Category
Article
ISSN
0021-8693

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✦ Synopsis

We present a Gröbner basis for the ideal of relations among the standard generators of the algebra of invariants of the special orthogonal group acting on k-tuples of vectors. The cases of SO 3 and SO 4 are interpreted in terms of the algebras of invariants and semi-invariants of k-tuples of 2 × 2 matrices. In particular, we present in an explicit form a Gröbner basis for the 2 × 2 matrix invariants. Finally we use a Sagbi basis to show that the algebra of SO 2 invariants is a Koszul algebra.

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