Related papers: On the source algebra equivalence class of blocks …

Let G be a finite group, and let B be a non-nilpotent block of G with respect to an algebraically closed field of characteristic 2. Suppose that B has an elementary abelian defect group of order 16 and only one simple module. The main…

We give a characterization of the sets of objects of the derived category of a block of a finite group algebra (or other symmetric algebra) that occur as the set of images of simple modules under an equivalence of derived categories. We…

The aim of this paper is to apply character properties of Frobenius group to a local block form of an group algebra. We start by establishing a block form of Brauer permutation Lemma by using block participation of conjugate classes of a…

Let $G$ be a finite group and $k$ a field of prime characteristic $p$. We examine the Lefschetz homomorphism $\Lambda: \mathcal{E}_k(G) \to O(T(kG))$ from the group of endotrivial complexes, i.e. the Picard group of the bounded homotopy…

The decomposition matrix of a finite group in prime characteristic p records the multiplicities of its p-modular irreducible representations as composition factors of the reductions modulo p of its irreducible representations in…

In this paper we study division algebras over the function fields of curves over $\Q_p$. The first and main tool is to view these fields as function fields over nonsingular $S$ which are projective of relative dimension 1 over the $p$ adic…

In this paper we complete the determination of the Brauer trees of unipotent blocks (with cyclic defect groups) of finite groups of Lie type. These trees were conjectured by the first author. As a consequence, the Brauer trees of principal…

We investigate the Brauer class of the endomorphism algebra of the motive attached to a non-CM form. The ramification of the algebra is shown in many cases to be controlled by the normalized slopes of the form.

We enumerate over even characteristic the components of the permutation module of the symmetric group of even degree acting on the set of its fixed point free involutions. We find the vertex and Brauer quotient for each component, and the…

Given a p-block B of a finite group with defect group P and fusion system F on P we show that the rank of the group P/foc(F) is invariant under stable equivalences of Morita type. The main ingredients are the star-construction, due to Broue…

In this paper, we prove that a \(p\)-block with abelian defect group is inertial if it covers a \(p\)-block of a normal subgroup of \(p\)-power index having only one irreducible Brauer character orbit.

We determine the blocks of the Brauer algebra in characteristic zero. We also give information on the submodule structure of standard modules for this algebra.

For any grading by an abelian group $G$ on the exceptional simple Lie algebra $\mathcal{L}$ of type $E_6$ or $E_7$ over an algebraically closed field of characteristic zero, we compute the graded Brauer invariants of simple…

Let $H$ be a Hopf algebra over a commutative ring $k$ with unity and $\sigma:H\otimes H\longrightarrow k$ be a cocycle on $H$. In this paper, we show that the Yetter-Drinfeld module category of the cocycle deformation Hopf algebra…

Necessary and sufficient conditions are given for a $G$-graded simple module over a unital associative algebra, graded by an abelian group $G$, to be isomorphic to a loop module of a simple module, as well as for two such loop modules to be…

The aim of this short research note is to present some results about a conjecture of Barker and Gelvin claiming that any source algebra of a block of a finite group has the unit group containing a basis stabilised by the left and right…

For finite groups $G$ with non-abelian, trivial intersection Sylow $p$-subgroups, the analysis of the Loewy structure of the centre of a block allows us to deduce that a stable equivalence of Morita type does not induce an algebra…

We show that the Green correspondence induces an injective group homomorphism from the linear source Picard group $\mathcal{L}(B)$ of a block $B$ of a finite group algebra to the linear source Picard group $\mathcal{L}(C)$, where $C$ is the…

Let G be a finite group, let N be a normal subgroup of G, and let theta in Irr(N) be a G-invariant character. We fix a prime p, and we introduce a canonical partition of Irr(G|theta) relative to p. We call each member B_theta of this…

One of the main problems in representation theory is to understand the exact relationship between Brauer corresponding blocks of finite groups. The case where the local correspondent has a unique simple module seems key. We characterize…