We determine the minimal lower bound n, with $$n \geqslant 1$$ , where n-th power of radical module category a representation-finite cluster tilted algebra vanishes. give such in terms number vertices underline quiver. Consequently, we get nilpotency index for self-injective algebras. also study non-zero composition m, $$m 2$$ irreducible morphisms between indecomposable modules algebras lying ...

The notion of level posets is introduced. This class of infinite posets has the property that between every two adjacent ranks the same bipartite graph occurs. When the adjacency matrix is indecomposable, we determine the length of the longest interval one needs to check to verify Eulerianness. Furthermore, we show that every level Eulerian poset associated to an indecomposable matrix has even ...

We study certain ltrations of indecomposable injective modules over classical Lie superalgebras, applying a general approach for noetherian rings developed by Brown, Jategaonkar, Lenagan, and Warreld. To indicate the consequences of our analysis, suppose that g is a complex classical simple Lie superalgebra and that E is an indecomposable injective g-module with nonzero (and so necessarily simp...

The category of finite dimensional (type 1) representations of a quantum affine algebra Uq(ĝ) is not semisimple. However, as any abelian category with finite-length objects, it admits a unique decomposition in a direct sum of indecomposable subcategories (blocks). We define the elliptic central character of a finite dimensional (type 1) representation of Uq(ĝ) and show that the block decomposit...

We prove that the number of right ideals of codimension n in the algebra of noncommutative Laurent polynomials in two variables over the finite field Fq is equal to (q − 1)q (n+1)(n−2) 2 ∑ θ q , where the sum is over all indecomposable permutations in Sn+1 and where inv(θ) stands for the number of inversions of θ. Mathematics Subject Classification Numbers: Primary: 05A15, Secondary: 05A19 Date...

Let Λ be an Auslander’s 1-Gorenstein Artinian algebra with global dimension 2. If Λ admits a trivial maximal 1-orthogonal subcategory of modΛ, then for any indecomposable module M ∈ modΛ, we have that the projective dimension of M is equal to 1 if and only if so is its injective dimension and that M is injective if the projective dimension of M is equal to 2, which implies that Λ is almost here...

Abstract Let k be an algebraically closed field of characteristic p > 2. We compute the Weyl filtration multiplicities in indecomposable tilting modules and decomposition numbers for symplectic group over terms cap-curl diagrams under assumption that is bigger than greatest hook length largest partition involved. As a corollary we obtain Brauer algebra same assumptions. Our work combines ide...