منابع مشابه
The transfer in modular invariant theory 1
We study the transfer homomorphism in modular invariant theory paying particular attention to the image of the transfer which is a proper non-zero ideal in the ring of invariants. We prove that, for a p-group over Fp whose ring of invariants is a polynomial algebra, the image of the transfer is a principal ideal. We compute the image of the transfer for SLn(Fq) and GLn(Fq) showing that both ide...
متن کاملThe Transfer in the Invariant Theory of Modular Permutation Representations
This note investigates the image of the transfer homomorphism for permutation representations of finite groups over finite fields. One obtains a number of results showing that the image of the transfer Im(Tr) together with certain Chern classes generate the ring of invariants as an algebra. By a careful analysis of orbit sums one finds the surprising fact that the ideal Im(Tr) is a prime ideal ...
متن کاملInvariant hypersurfaces for derivations in positive characteristic
Let A be an integral k-algebra of finite type over an algebraically closed field k of characteristic p > 0. Given a collection D of k-derivations on A, that we interpret as algebraic vector fields on X = Spec(A), we study the group spanned by the hypersurfaces V (f) of X invariant under D modulo the rational first integrals of D. We prove that this group is always a finite dimensional Fp-vector...
متن کاملFlow-Invariant Hypersurfaces in Semi-Dispersing Billiards
This work results from our attempts to solve Boltzmann–Sinai’s hypothesis about the ergodicity of hard ball gases. A crucial element in the studies of the dynamics of hard balls is the analysis of special hypersurfaces in the phase space consisting of degenerate trajectories (which lack complete hyperbolicity). We prove that if a flow-invariant hypersurface J in the phase space of a semi-disper...
متن کاملAn Invariant for Hypersurfaces in Prime Characteristic
A hypersurface of order (n+ 1)(ph − 1) in projective space of dimension n of prime characteristic p has an invariant monomial. This implies that a hypersurface of order (n+1)(ph−1)−1 determines an invariant point. A hypersurface of order d < n+ 1 in a projective space of dimension n of characteristic two has an invariant set of subspaces of dimension d− 1 determined by one linear condition on t...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2006
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2006.05.005