Related papers: On centers of blocks with one simple module

We investigate the source algebra class of a p-block with cyclic defect groups of the group algebra of a finite group. By the work of Linckelmann this class is parametrized by the Brauer tree of the block together with a sign function on…

The notion of the center of an algebra over a field k has a far reaching generalization to algebras in monoidal categories. The center then lives in the monoidal center of the original category. This generalization plays an important role…

We give the very first example of a simple $2-(81,6,2)$ design. Its points are the elements of the elementary abelian group of order 81 and each block is the union of two parallel lines of the 4-dimensional geometry over the field of order…

The aim of this paper is to present a complete description of the structure of subsets S of an orderable group G satisfying |S^2| = 3|S|-2 and <S> is non-abelian.

In this paper we classify all blocks with defect group $C_{2^n}\times C_2\times C_2$ up to Morita equivalence. Together with a recent paper of Wu, Zhang and Zhou, this completes the classification of Morita equivalence classes of $2$-blocks…

Let $\mathcal{C}:=\mathcal{C}(G,\omega,H,\psi)$ be a finite group scheme-theoretical category over an algebraically closed field of characteristic $p\ge 0$ as defined by the first author. For any indecomposable exact module category over…

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 exhibit a simple construction, based on elementary linear algebra, for a class of examples of finite $p$-groups of nilpotence class $2$ all of whose automorphisms are central.

We discuss an algebraic treatment of four-body clusters which includes both continuous and discrete symmetries. In particular, tetrahedral configurations with T(d) symmetry are analyzed with respect to the energy spectrum, transition form…

A differential algebra of finite type over a field k is a filtered algebra A, such that the associated graded algebra is finite over its center, and the center is a finitely generated k-algebra. The prototypical example is the algebra of…

We give an example of a finite-dimensional algebra with a 2-cluster tilting module and a simple module which has infinite complexity. This answers a question of Erdmann and Holm.

We characterize the structure of a seven-dimensional Lie algebra with non-trivial center endowed with a closed G$_2$-structure. Using this result, we classify all unimodular Lie algebras with non-trivial center admitting closed…

A maximal abelian normal subgroup A in a nilpotent group N is self-centralizing. This makes their role an important one in determining the structure of the nilpotent group. For example if A is finite then N is also finite. In the free…

This article undertakes an exploration of simple modules of 3-cyclic quantum Weyl algebra at roots of unity. Under the roots of unity assumption, the algebra becomes a Polynomial Identity algebra and the vector space dimension of the simple…

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…

Let $A$ be an algebra over a commutative ring $k$. We compute the center of the category of $A$-bimodules. There are six isomorphic descriptions: the center equals the weak center, and can be described as categories of noncommutative…

In this paper, we prove that if $G$ is a finite group in which elements of the same order outside the center are conjugate, then $G$ is abelian or is isomorphic to $S_3$, the symmetry group of degree 3.

Let A be a standard graded Artinian algebra over a field of characteristic zero and let z be a linear form in A. We define the central simple modules for each such pair (A, z). Assume that A is Gorenstein. Then we prove that A has the…

For any block of a finite group over an algebraically closed field of characteristic $2$ which has dihedral, semidihedral, or generalized quaternion defect groups, we determine explicitly the decomposition of the associated diagonal…

We conjecture that the "nilpotent points" of Calogero-Moser space for reflection groups are parametrised naturally by the two-sided cells of the group with unequal parameters. The nilpotent points correspond to blocks of restricted…