Let n be a positive integer and λ partition of . M the Young permutation module labelled by In this paper, we study symmetric exterior powers in characteristic case. We determine that are projective. All indecomposable also classified. then prove some results for direct summands have largest complexity sum decompositions end parameterizing all Scott modules isomorphic to or square determining t...

Abstract For a finite-dimensional Hopf algebra $\mathsf {A}$ , the McKay matrix {M}_{\mathsf {V}}$ of an -module {V}$ encodes relations for tensoring simple -modules with . We prove results about eigenvalues and right left (generalized) eigenvectors by relating them to characters. show how projective {Q}_{\mathsf obtained indecomposable modules is related dual module illustrate these Drinfeld d...

We give a sufficient condition for the $kG$-Scott module with vertex $P$ to remain indecomposable under taking Brauer construction any subgroup $Q$ of as $k[Q\,C_G(Q)]$-module, where $k$ is field characteristic $2$, and wreathed $2$-subgroup finite group $G$. This generalizes results cases abelian some others. The motivation this paper that indecomposability $p$-permutation bimodule ($p$ prime)...

We study the homotopy category K(InjA) of all injective A-modules InjA and derived category D(ModA) of the category ModA of all A-modules, where A is finite dimensional algebra over an algebraically closed field. We are interested in the algebra with discrete derived category (derived discrete algebra. For a derived discrete algebra A, we get more concrete properties of K(InjA) and D(ModA). The...

Let G be a nite group and k an algebraically closed eld of characteristic p. Let F U be the Rickard idempotent kG-module corresponding to the set U of subvarieties of the cohomology variety VG which are not irreducible components. We show that F U is a nite sum of generic modules corresponding to the irreducible components of VG. In this context, a generic module is an indecomposable module of ...

Abstract For a Galois extension $K/F$ with $\text {char}(K)\neq 2$ and $\mathrm {Gal}(K/F) \simeq \mathbb {Z}/2\mathbb {Z}\oplus {Z}$ , we determine the $\mathbb {F}_{2}[\mathrm {Gal}(K/F)]$ -module structure of $K^{\times }/K^{\times 2}$ . Although there are an infinite number (pairwise nonisomorphic) indecomposable {F}_{2}[\mathbb {Z}]$ -modules, our decomposition includes at most nine types....

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 ...