English

Doset Hibi rings with an application to invariant theory

Commutative Algebra 2017-02-27 v4

Abstract

We define the concept of a doset Hibi ring and a generalized doset Hibi ring which are subrings of a Hibi ring and are normal affine semigrouprings. We apply the theory of (generalized) doset Hibi rings to analyze the rings of absolute orthogonal invariants and absolute special orthogonal invariants and show that these rings are normal and Cohen-Macaulay and has rational singularities if the characteristic of the base field is zero and is F-rational otherwise. We also state criteria of Gorenstein property of these rings.

Keywords

Cite

@article{arxiv.0901.1052,
  title  = {Doset Hibi rings with an application to invariant theory},
  author = {Mitsuhiro Miyazaki},
  journal= {arXiv preprint arXiv:0901.1052},
  year   = {2017}
}

Comments

We added a down to earth proof of the result of DeConcini and Procesi about the rings of absolute orthogonal invariants and absolute special orthogonal invariants

R2 v1 2026-06-21T11:58:44.095Z