Related papers: Module schemes in invariant theory

Given a cycle module M with a ring structure we show that the cycle complex with coefficients in M of a smooth scheme of finite type over a field has a A-infinity algebra structure. In the case of Milnor K-theory this gives a homotopy model…

In this paper, we define an invariant, which we believe should be the substitute for total K-theory in the case when there is one distinguished ideal. Moreover, some diagrams relating the new groups to the ordinary K-groups with…

We study from an algebraic point of view the question of extending an action of a group \(\Gamma\) on a commutative domain \(R\) to a formal pseudodifferential operator ring \(B=R(\!(x\,;\,d)\!)\) with coefficients in \(R\), as well as to…

Let $Y$ denote a $D$-class symmetric association scheme with $D \geq 3$, and suppose $Y$ is almost-bipartite P- and Q-polynomial. Let $x$ denote a vertex of $Y$ and let $T=T(x)$ denote the corresponding Terwilliger algebra. We prove that…

Let $k$ be a field and $G \subseteq Gl_n(k)$ be a finite group with $|G|^{-1} \in k$. Let $G$ act linearly on $A = k[X_1, \ldots, X_n]$ and let $A^G$ be the ring of invariant's. Suppose there does not exist any non-trivial one-dimensional…

If the inverse of a nonsingular polynomial matrix $L$ has a polynomial part then one can associate with $L$ a module over the ring of proper rational functions, which is related to the structure of $L$ at infinity. In this paper we…

We study relations between the classical modular symbols associated with congruence subgroups and Kontsevich-Pestun-Tschinkel groups $\mathcal{M}_n(G)$ associated with finite abelian groups $G$.

Let $R$ be a commutative noetherian local ring. We define a new invariant for $R$-modules which we call the little dimension. Using it, we extend the improved new intersection theorem.

Every quotient R/I of a semigroup ring R by a radical monomial ideal I has a unique minimal injective-like resolution by direct sums of quotients of R modulo prime monomial ideals. The quotient R/I is Cohen-Macaulay if and only if every…

For a scheme S with a good action of a finite abelian group G having enough roots of unity we show that the quotient map on the G-equivariant Grothendieck ring of varieties over S is well defined with image in the Grothendieck ring of…

Let $R$ be a finite ring and let $M, N$ be two finite left $R$-modules. We present two distinct deterministic algorithms that decide in polynomial time whether or not $M$ and $N$ are isomorphic, and if they are, exhibit an isomorphism. As…

Over an algebraically closed base field $k$ of characteristic 2, the ring $R^G$ of invariants is studied, $G$ being the orthogonal group O(n) or the special orthogonal group SO(n) and acting naturally on the coordinate ring $R$ of the…

In this paper, we introduce initially Cohen-Macaulay modules over a commutative Noetherian local ring $R$, a new class of $R$-modules that generalizes both Cohen-Macaulay and sequentially Cohen-Macaulay modules. A finitely generated…

We investigate the Cohen-Macaulay property for rings of invariants under multiplicative actions of a finite group $G$. By definition, these are $G$-actions on Laurent polynomial algebras that stabilize the multiplicative group consisting of…

This note shows that the module of smooth vector fields on ${\mathbb{R}}^n$, which are invariant under the linear action of a compact Lie group $G$ is finitely generated by polynomial vector fields on ${\mathbb{R}}^n$ which are invariant…

Three new knot invariants are defined using cocycles of the generalized quandle homology theory that was proposed by Andruskiewitsch and Gra\~na. We specialize that theory to the case when there is a group action on the coefficients. First,…

We consider the 2-generated free metabelian associative and Lie algebras over the complex field and the invariants of the dihedral groups of finite order acting on these algebras. In the associative case we find a finite set of generators…

We construct a noncommutative desingularization of the discriminant of a finite reflection group $G$ as a quotient of the skew group ring $A=S*G$. If $G$ is generated by order two reflections, then this quotient identifies with the…

A question of Bergman asks whether the adjoint of the generic square matrix over a field can be factored nontrivially as a product of square matrices. We show that such factorizations indeed exist over any coefficient ring when the matrix…

Counterparts of several classical results of number theory are proven for the ring of polynomials with coefficients in a number field. A theorem of Milnor that determines the Witt ring of a function field is applied to prove an analogue of…