Related papers: Invariant rings through categories
For any length category, we establish a set of rules (necessary and sufficient) that ensure a partial order on the isomorphism classes of simple objects such that the category is equivalent to the category of finite dimensional…
Nagata's famous counterexample to Hilbert's fourteenth problem shows that the ring of invariants of an algebraic group action on an affine algebraic variety is not always finitely generated. In some sense, however, invariant rings are not…
We introduce an approach to the categorification of rings, via the notion of distributive categories with negative objects, and use it to lay down categorical foundations for the study of super, quantum and non-commutative combinatorics.…
We focus on working on incidence rings, a class of (possibly infinite) matrix rings indexed by ordered sets. Some general properties about them are given, including how they are always the inverse limit of finite matrix rings, giving a…
Let G be a finite group acting linearly on the polynomial ring with invariant ring R. If the action is small, then a classical result of Auslander gives in dimension two a correspondence between linear representations of G and maximal…
The classical theorems relating integral binary quadratic forms and ideal classes of quadratic orders have been of tremendous importance in mathematics, and many authors have given extensions of these theorems to rings other than the…
The first part of this paper is a refinement of Winkelmann's work on invariant rings and quotients of algebraic groups actions on affine varieties, where we take a more geometric point of view. We show that the (algebraic) quotient…
We describe the rings of invariants for the finite orthogonal groups of plus type in odd characteristic acting on the defining representations. We also describe the invariants of the corresponding Sylow subgroups in the defining…
We describe necessary and sufficient conditions for the hereditarity of the category algebra of an infinite EI category satisfying certain combinatorial assumptions. More generally, we discuss conditions such that the left global dimension…
Let $\mathfrak{R}$ be a weakly noetherian variety of unitary associative algebras (over a field $K$ of characteristic 0), i.e., every finitely generated algebra from $\mathfrak{R}$ satisfies the ascending chain condition for two-sided…
For a commutative ring $A$, we have the category of (bounded-below) chain complexes of $A$-modules $Ch_{+}(A\mymod)$, a closed symmetric monoidal category with a compatible stable Quillen model structure. The associated homotopy category is…
We extend the comatrix coring to the case of a quasi-finite bicomodule. We also generalize some of its interesting properties. We study equivalences between categories of comodules over rather general corings. We particularize to the case…
Let $A$ be a finite or countable alphabet and let $\theta$ be literal (anti)morphism onto $A^*$ (by definition, such a correspondence is determinated by a permutation of the alphabet). This paper deals with sets which are invariant under…
We call a finitely complete category algebraically coherent when the change-of-base functors of its fibration of points are coherent, which means that they preserve finite limits and jointly strongly epimorphic pairs of arrows. We give…
Although there is no natural internal product for hermitian forms over an algebra with involution of the first kind, we describe how to multiply two $\varepsilon$-hermitian forms to obtain a quadratic form over the base field. This allows…
We classify thick subcategories of the $\infty$-categories of perfect modules over ring spectra which arise as functions on even periodic derived stacks satisfying affineness and regularity conditions. For example, we show that the thick…
The work proves that, for three-dimensional upper triangular groups over a field of odd characteristic with an abelian unipotent subgroup, the ring of invariants is polynomial if and only if the unipotent subgroup is generated by…
When we consider a finite abelian group acting linearly on a polynomial ring, we can find monomial generators for the subring of invariants. By Noether's degree bound and Hilbert's finiteness theorem, we know that there are finitely many…
In this paper, we shall consider some finiteness of ind-sheaves with ring actions. As the main result of this paper, there exists an equivalence of categories between the abelian category of coherent ind-$\beta\mathcal{A}$-modules and the…
Given a commutative ring $R$ and finitely generated ideal $I$, one can consider the classes of $I$-adically complete, $L_0^I$-complete and derived $I$-complete complexes. Under a mild assumption on the ideal $I$ called weak pro-regularity,…