ترغب بنشر مسار تعليمي؟ اضغط هنا

Separating invariants for arbitrary linear actions of the additive group

147   0   0.0 ( 0 )
 نشر من قبل Jonathan Elmer
 تاريخ النشر 2013
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

We consider an arbitrary representation of the additive group over a field of characteristic zero and give an explicit description of a finite separating set in the corresponding ring of invariants.



قيم البحث

اقرأ أيضاً

The study of separating invariants is a recent trend in invariant theory. For a finite group acting linearly on a vector space, a separating set is a set of invariants whose elements separate the orbits of G. In some ways, separating sets often exhib it better behavior than generating sets for the ring of invariants. We investigate the least possible cardinality of a separating set for a given G-action. Our main result is a lower bound that generalizes the classical result of Serre that if the ring of invariants is polynomial then the group action must be generated by pseudoreflections. We find these bounds to be sharp in a wide range of examples.
Affine ind-varieties are infinite dimensional generalizations of algebraic varieties which appear naturally in many different contexts, in particular in the study of automorphism groups of affine spaces. In this article we introduce and develop the b asic algebraic theory of topologically integrable derivations of complete topological rings. We establish a bijective algebro-geometric correspondence between additive group actions on affine ind-varieties and topologically integrable derivations of their coordinate pro-rings which extends the classical fruitful correspondence between additive group actions on affine varieties and locally nilpotent derivations of their coordinate rings.
We establish basic properties of a sheaf of graded algebras canonically associated to every relative affine scheme $f : X rightarrow S$ endowed with an action of the additive group scheme $mathbb{G}_{ a,S}$ over a base scheme or algebraic space $S$, which we call the (relative) Rees algebra of the $mathbb{G}_{ a,S}$-action. We illustrate these properties on several examples which played important roles in the development of the algebraic theory of locally nilpotent derivations and give some applications to the construction of families of affine threefolds with Ga-actions.
210 - Steven Hurder , Olga Lukina 2019
A Cantor action is a minimal equicontinuous action of a countably generated group G on a Cantor space X. Such actions are also called generalized odometers in the literature. In this work, we introduce two new conjugacy invariants for Cantor actions, the stabilizer limit group and the centralizer limit group. An action is wild if the stabilizer limit group is an increasing sequence of stabilizer groups without bound, and otherwise is said to be stable if this group chain is bounded. For Cantor actions by a finitely generated group G, we prove that stable actions satisfy a rigidity principle, and furthermore show that the wild property is an invariant of the continuous orbit equivalence class of the action. A Cantor action is said to be dynamically wild if it is wild, and the centralizer limit group is a proper subgroup of the stabilizer limit group. This property is also a conjugacy invariant, and we show that a Cantor action with a non-Hausdorff element must be dynamically wild. We then give examples of wild Cantor actions with non-Hausdorff elements, using recursive methods from Geometric Group Theory to define actions on the boundaries of trees.
230 - Bingbing Liang , Kesong Yan 2011
We define the topological pressure for any sub-additive potentials of the countable discrete amenable group action and any given open cover. A local variational principle for the topological pressure is established.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا