منابع مشابه
Separating invariants
This paper studies separating subsets of an invariant ring or, more generally, of any set consisting of functions. We prove that a subset of a finitely generated algebra always contains a finite separating subset. We also show that a general version of Noether’s degree bound holds for separating invariants, independently of the characteristic. The paper also contains a conceptual investigation ...
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We prove a characteristic free version of Weyl’s theorem on polarization. Our result is an exact analogue of Weyl’s theorem, the difference being that our statement is about separating invariants rather than generating invariants. For the special case of finite group actions we introduce the concept of cheap polarization, and show that it is enough to take cheap polarizations of invariants of j...
متن کاملSeparating Invariants and Finite Reflection Groups
Roughly speaking, a separating algebra is a subalgebra of the ring of invariants whose elements distinguish between any two orbits that can be distinguished using invariants. In this paper, we introduce a more geometric notion of separating algebra. This allows us to prove that when there is a polynomial separating algebra, the group is generated by reflections, and when there is a complete int...
متن کاملExplicit separating invariants for cyclic P-groups
We consider a finite dimensional indecomposable modular representation of a cyclic p-group and we give a recursive description of an associated separating set: We show that a separating set for a representation can be obtained by adding to a separating set for any subrepresentation some explicitly defined invariant polynomials. Meanwhile, an explicit generating set for the invariant ring is kno...
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We consider an arbitrary representation of the additive group Ga over a field of characteristic zero and give an explicit description of a finite separating set in the corresponding ring of invariants.
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ژورنال
عنوان ژورنال: Transformation Groups
سال: 2007
ISSN: 1083-4362,1531-586X
DOI: 10.1007/s00031-005-1131-4