@article {Domokos:2001-09-01T00:00:00:0021-8693:706,
author = "Domokos, M. and Drensky, V.",
title = "Gröbner Bases for the Rings of Special Orthogonal and 2 × 2 Matrix Invariants",
journal = "Journal of Algebra",
volume = "243",
number = "2",
year = "2001-09-01T00:00:00",
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 **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.",
pages = "706-716",
url = "http://www.ingentaconnect.com/content/ap/ja/2001/00000243/00000002/art08820",
keyword = "standard tableaux, ring of invariants, special orthogonal group, Grö, bner basis"
}