Related papers: Low dimensional projective indecomposable modules …

In this paper, we study the Chevalley property of Cayley-Hamilton Hopf algebras in the sense of De Concini-Procesi-Reshetikhin-Rosso using discriminant ideals. For any affine Cayley-Hamilton Hopf algebra $(H,C,\text{tr})$ whose identity…

We establish a theorem concerning the commuting scheme in characteristic p. As a significant application of this theorem, we derive an explicit lower bound for the characteristic p, ensuring the validity of the higher-dimensional Chevalley…

A famous result due to L. S. Levy provides a classification of all finitely generated indecomposable modules over Dedekind-like rings. This motivates us to outline an approach to the classification of indecomposable pseudo-absorbing primary…

It is proved that an irreducible quasifinite $W_\infty$-module is a highest or lowest weight module or a module of the intermediate series; a uniformly bounded indecomposable weight $W_\infty$-module is a module of the intermediate series.…

We prove a decomposition of definable groups in o-minimal structures generalizing the Jordan-Chevalley decomposition of linear algebraic groups. It follows that any definable linear group G is a semidirect product of its maximal normal…

An algebraic classification is given for spaces of holomorphic vector-valued modular forms of arbitrary real weight and multiplier system, associated to irreducible, T-unitarizable representations of the full modular group, of dimension…

Let $\F_q$ be a field of characteristic $p$ with $q$ elements. It is known that the degrees of the irreducible characters of the Sylow $p$-subgroup of $GL_n(\F_q)$ are powers of $q$ by Issacs. On the other hand Sangroniz showed that this is…

We describe the semisimplification of the monoidal category of tilting modules for the algebraic group GL_n in characteristic p > 0. In particular, we compute the dimensions of the indecomposable tilting modules modulo p.

Following Gluck and Wolf we complete the It\^o--Michler's Theorem for the projective representations of a $p$-solvable or $\pi$-separable group, and then we relate the projective irreducible modules of such a group with those of its Sylow…

Let $G$ be a finite group and $k$ a field of characteristic $p > 0$. Balmer and Gallauer's recent result on finite $p$-permutation resolutions of $kG$-modules motivates the study of an intriguing new invariant; the $p$-permutation…

Brou\'e, Malle and Michel have shown that the automizer of an abelian Sylow p-subgroup in a finite simple Chevalley group is an irreducible complex reflection group, for p not too small and different from the defining characteristic. The…

We prove a higher-dimensional Chevalley restriction theorem for orthogonal groups, which was conjectured by Chen and Ng\^{o} for reductive groups. In characteristic $p>2$, we also prove a weaker statement. In characteristic $0$, the theorem…

We compute the Loewy structure of the indecomposable projective modules for the group algebra FG, where G is the alternating group on 10 letters and F is an algebraically closed field of characteristic 3.

We give a lower bound of the Loewy length of the projective cover of the trivial module for the group algebra $kG$ of a finite group $G$ of Lie type defined over a finite field of odd characteristic $p$, where $k$ is an arbitrary field of…

G. Navarro raised the question under what circumstancs two vertices of two indecomposable modules over a finite group algebra generate a Sylow $p$-subgroup. The present note provides a sufficient criterion for when this is the case. This…

We classify the simple quantum group modules with finite dimensional weight spaces when the quantum parameter $q$ is transcendental and the Lie algebra is not of type $G_2$. This is part $2$ of the story. The first part being Irreducible…

We address two aspects of finitely generated modules of finite projective dimension over local rings and their connection in between: embeddability and grade of order ideals of minimal generators of syzygies. We provide a solution of the…

Let $g$ be a finite dimensional simple Lie algebra. Denote by $\mathcal B$ the category of all bounded weight $g$-modules, i.e. those which are direct sum of their weight spaces and have uniformly bounded weight multiplicities. A result of…

We investigate finite non-Abelian simple groups $G$ for which the projective cover of the trivial module coincides with the permutation module on a subgroup and classify all cases unless $G$ is of Lie type in defining characteristic.

For any affine Hopf algebra $H$ which admits a large central Hopf subalgebra, $H$ can be endowed with a Cayley-Hamilton Hopf algebra structure in the sense of De Concini-Procesi-Reshetikhin-Rosso. The category of finite-dimensional modules…