INVARIANT RINGS OF ORTHOGONAL GROUPS OVER ${\mathbb F}_2$
Glasgow mathematical journal, Tome 47 (2005) no. 1, pp. 7-54
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We determine the rings of invariants $S^G$ where $S$ is the symmetric algebra on the dual of a vector space $V$ over ${\mathbb F}_2$ and $G$ is the orthogonal group preserving a non-singular quadratic form on $V$. The invariant ring is shown to have a presentation in which the difference between the number of generators and the number of relations is equal to the minimum possibility, namely $\dim V$, and it is shown to be a complete intersection. In particular, the rings of invariants computed here are all Gorenstein and hence Cohen-Macaulay.
KROPHOLLER, P. H.; RAJAEI, S. MOHSENI; SEGAL, J. INVARIANT RINGS OF ORTHOGONAL GROUPS OVER ${\mathbb F}_2$. Glasgow mathematical journal, Tome 47 (2005) no. 1, pp. 7-54. doi: 10.1017/S0017089504002198
@article{10_1017_S0017089504002198,
author = {KROPHOLLER, P. H. and RAJAEI, S. MOHSENI and SEGAL, J.},
title = {INVARIANT {RINGS} {OF} {ORTHOGONAL} {GROUPS} {OVER} ${\mathbb F}_2$},
journal = {Glasgow mathematical journal},
pages = {7--54},
year = {2005},
volume = {47},
number = {1},
doi = {10.1017/S0017089504002198},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089504002198/}
}
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AU - KROPHOLLER, P. H.
AU - RAJAEI, S. MOHSENI
AU - SEGAL, J.
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JO - Glasgow mathematical journal
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