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

Authors: Domokos M.¹; Drensky V.²

Source: Journal of Algebra, Volume 243, Number 2, September 2001 , pp. 706-716(11)

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Abstract:

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 SO₃ and SO₄ 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 SO₂ invariants is a Koszul algebra. Copyright 2001 Academic Press.

Keywords: special orthogonal group; ring of invariants; Grö; bner basis; standard tableaux

Language: English

Document Type: Research article

Affiliations: 1: Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, 1364, Hungary 2: Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Akad. G. Bonchev Str., Block 8, Sofia, 1113, Bulgaria

Publication date: 2001-09-01