Related papers: Construction of Rank $2$ Indecomposable Modules in…

We study decomposable N^d-indexed persistence modules via higher dimensional partitions. Their barcodes are defined in terms of the extended interior of the corresponding Young diagrams. For two decomposable N^d-indexed persistence modules,…

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…

Let $\preceq$ be a compatible total order on the additive group $\mathbb{Z}^2$, and $L$ be the rank two Heisenberg-Virasoro algebra. For any $\mathbf{c}=(c_1,c_2,c_3,c_4) \in \mathbb{C}^4$, we define $\mathbb{Z}^2$-graded Verma module…

Auslander and Reiten called a finite dimensional algebra $A$ over a field Cohen-Macaulay if there is an $A$-bimodule $W$ which gives an equivalence between the category of finitely generated $A$-modules of finite projective dimension and…

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…

In this paper, we associate a new topology to a nonzero unital module $M$ over a commutative $R$, which is called Golomb topology of the $R$-module $M$. Let $M\ $be an\ $R$-module and $B_{M}$ be the family of coprime cosets $\{m+N\}$ where…

We study two categories of ${U}(\mathfrak h)$-free $\mathfrak{sl}(m|n)$-modules of total rank 2: $\mathcal{M}_{\mathfrak{sl}(m|n)}(2)$, whose objects are free of rank 2 over ${U}(\mathfrak h)$ which are not necessarily $\mathbb Z_2$-graded,…

Let $H$ be a finite dimensional pointed rank one Hopf algebra of nilpotent type. We first determine all finite dimensional indecomposable $H$-modules up to isomorphism, and then establish the Clebsch-Gordan formulas for the decompositions…

In the first part of this paper we construct a model structure for the category of filtered cochain complexes of modules over some commutative ring $R$ and explain how the classical Rees construction relates this to the usual projective…

There is a long-standing belief that the modular tensor categories $\mathcal{C}(\mathfrak{g},k)$, for $k\in\mathbb{Z}_{\geq1}$ and finite-dimensional simple complex Lie algebras $\mathfrak{g}$, contain exceptional connected \'etale algebras…

If $(A,\mathfrak{m})$ is a hypersurface ring of dimension $d$ with $e(A)=3$. Let $M$ be an MCM $A$-module with $\mu(M)=4$ then we prove that $\depth{G(M)}\geq d-3$.

Let R be a commutative Noetherian ring, a a proper ideal of R and M a finite R-module. It is shown that, if (R;m) is a complete local ring, then under certain conditions a contains a regular element on DR(Hc a(M)), where c = cd(a;M). A…

Given a finite group scheme $\cG$ over an algebraically closed field $k$ of characteristic $\Char(k)=p>0$, we introduce new invariants for a $\cG$-module $M$ by associating certain morphisms $\deg^j_M : U_M \lra \Gr_d(M) \ \…

For $k = 1, 2,...,n-1$ let $V_k = V(\lambda_k)$ be the Weyl module for the special orthogonal group $G = \mathrm{SO}(2n+1,\F)$ with respect to the $k$-th fundamental dominant weight $\lambda_k$ of the root system of type $B_n$ and put $V_n…

In this paper we give a diagrammatic description of the categories of modules coming from the conformal embeddings $\mathcal{V}(\mathfrak{sl}_N,N) \subset \mathcal{V}(\mathfrak{so}_{N^2-1},1)$. A small variant on this construction (morally…

If R is a commutative ring, we prove that every finitely generated module has a pure-composition series with indecomposable factors and any two such series are isomorphic if and only if R is a Bezout ring and a CF-ring.

Previously, the last two authors found large families of decomposable Specht modules labelled by bihooks, over the Iwahori--Hecke algebra of type $B$. In most cases we conjectured that these were the only decomposable Specht modules…

ABSTRACT. Let $\Phi$ be a finite dimensional $K$-algebra and let $\mathscr{C} = \textrm{mod}\: \Phi$ be the abelian category of finitely generated right $\Phi$-modules. In their 1985 paper ``Modules determined by their composition…

Local conditions for the direct summands of a persistence module to belong to a certain class of indecomposables have been proposed in the 2-parameter setting, notably for the class of indecomposables called block modules, which plays a…

This paper is the first of a pair that aims to classify a large number of the type $II$ quantum subgroups of the categories $\mathcal{C}(\mathfrak{sl}_{r+1},k)$. In this work we classify the braided auto-equivalences of the categories of…