Rings of invariants of modular p-groups which are hypersurfaces
نویسندگان
چکیده
منابع مشابه
Computing Modular Invariants of p-groups
Let V be a finite dimensional representation of a p-group, G, over a field, k, of characteristic p. We show that there exists a choice of basis and monomial order for which the ring of invariants, k[V ]G, has a finite SAGBI basis. We describe two algorithms for constructing a generating set for k[V ]G. We use these methods to analyse k[2V3]3 where U3 is the p-Sylow subgroup of GL3(Fp) and 2V3 i...
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∗ We initiate a study of the rings of invariants of modular representations of elementary abelian p-groups. With a few notable exceptions, the modular representation theory of an elementary abelian p-group is wild. However, for a given dimension, it is possible to parameterise the representations. We describe parameterisations for modular representations of dimension two and of dimension three....
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We study separating algebras for rings of invariants of finite groups. We describe a separating subalgebra for invariants of p-groups in characteristic p using only transfers and norms. Also we give an explicit construction of a separating set for invariants of groups acting diagonally. Let F be an algebraically closed field and let G be a finite group. Consider a faithful representation ρ : G ...
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In this paper, a new algorithm for computing secondary invariants of invariant rings of monomial groups is presented. The main idea is to compute simultaneously a truncated SAGBI-G basis and the standard invariants of the ideal generated by the set of primary invariants. The advantage of the presented algorithm lies in the fact that it is well-suited to complexity analysis and very easy to i...
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We shall prove the fundamental results of Hilbert and Noether for invariant subrings of finite subgroups of the general linear groups in the non-modular case, i.e. when the field has characteristic zero or coprime with the order of the group. We will also derive the Molien’s formula for the Hilbert series of the ring of invariants. We will show, through examples, that the Molien’s formula helps...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2005
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2005.05.026