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- Title
Archimedean Orders on Certain Rings of Invariants.
- Authors
Tesemma, Mohammed; Wang, Haohao; Arad, Z.
- Abstract
Let $\mathcal{G}\leq {\rm GL}_n (\mathbb{Z})$ act multiplicatively on the Laurent polynomial algebra k[x± 1] in n indeterminates x={x1, ...,xn}. Consider the initial algebra of the ring of invariants $k[\textbf{x}^{\pm1}]^{\mathcal{G}}$ with respect to some monomial order. We set a sufficient condition on $\mathcal{G}$ such that each initial algebra is represented by some weight vectors in ℝn. We also show that the condition is necessary in the case where the rank n = 2.
- Subjects
REFLECTION groups; ASSOCIATIVE rings; POLYNOMIALS; INVARIANTS (Mathematics); VECTOR spaces; NUMERICAL analysis
- Publication
Algebra Colloquium, 2011, Vol 18, Issue 2, p289
- ISSN
1005-3867
- Publication type
Article
- DOI
10.1142/S1005386711000186