Nakashima, Norihiro Tsujie, Shuhei
Published in
Journal of Algebra

A canonical system of basic invariants is a system of invariants satisfying a set of differential equations. The properties of a canonical system are related to the mean value property for polytopes. In this article, we naturally identify the vector space spanned by a canonical system of basic invariants with an invariant space determined by a fund...

Published in
Journal of Algebra

Acciarri, Cristina Shumyatsky, Pavel
Published in
Journal of Algebra

The coprime commutators γj⁎ and δj⁎ were recently introduced as a tool to study properties of finite groups that can be expressed in terms of commutators of elements of coprime orders. Every element of a finite group G is both a γ1⁎-commutator and a δ0⁎-commutator. Now let j⩾2 and let X be the set of all elements of G that are powers of γj−1⁎-commu...

Chau, Tran Do Minh Nhan, Le Thanh
Published in
Journal of Algebra

Let (R,m) be a Noetherian local ring and M a finitely generated R-module. It is well known that the local cohomology module Hmi(M) is Artinian for all i⩾0. Following I.G. Macdonald [8], denote by AttRHmi(M) the set of attached primes of Hmi(M). This paper is concerned with clarifying the structure of the base ring R via a relation between AttRHmi(M...

Shchigolev, Vladimir
Published in
Journal of Algebra

We give an exact algorithm to calculate (under some GKM-restriction) the matrix describing the embedding B(s)x⊂B(s)x, where the first module is the costalk and the second one is the stalk at x of a Bott–Samelson module (sheaf) B(s). This allows us to calculate the first few terms of the decomposition of B(s) into a sum of indecomposable modules (sh...

Carlini, Enrico Guardo, Elena Van Tuyl, Adam
Published in
Journal of Algebra

Let F be a homogeneous polynomial in S=C[x0,…,xn]. Our goal is to understand a particular polynomial decomposition of F; geometrically, we wish to determine when the hypersurface defined by F in Pn contains a star configuration. To solve this problem, we use techniques from commutative algebra and algebraic geometry to reduce our question to comput...

Blasiak, Jonah
Published in
Journal of Algebra

Let Hr be the generic type A Hecke algebra defined over Z[u,u−1]. The Kazhdan–Lusztig bases {Cw}w∈Sr and {Cw′}w∈Sr of Hr give rise to two different bases of the Specht module Mλ, λ⊢r, of Hr. These bases are not equivalent and we show that the transition matrix S(λ) between the two is the identity at u=0 and u=∞. To prove this, we first prove a simi...

Poizat, Bruno
Published in
Journal of Algebra

Given a subroup G of a stable (in the model-theoric sense) group Γ, in particular when Γ is a group of finite Morley rank, the traces on G of the definable subsets of Γ have a remarkable property: if the definable closure of G is connected, they are either supergeneric, or supergenerically complemented, in the sense of the definition given at the v...

Kubik, Bethany Leamer, Micah Sather-Wagstaff, Sean
Published in
Journal of Algebra

Let R be a commutative ring, and let L and L′ be R-modules. We investigate finiteness conditions (e.g., noetherian, artinian, mini-max, Matlis reflexive) of the modules ExtRi(L,L′) and ToriR(L,L′) when L and L′ satisfy combinations of these finiteness conditions. For instance, if R is noetherian, then given R-modules M and M′ such that M is Matlis ...

Sivatski, A.S.
Published in
Journal of Algebra

Let k be a field of characteristic distinct from 2, V a finite dimensional vector space over k. We call two pairs of quadratic k-forms (f1,g1), (f2,g2) on V isomorphic if there exists an isomorphism s:V→V such that f2=f1∘s, g2=g1∘s. We prove that if f1+tg1≃f2+tg2 over k(t) and either the form f1+tg1 is anisotropic, or det(f1+tg1) is a squarefree po...