The Loewy structure of projective indecomposable modules for some modular group algebras

A deformation-theoretic version of Maschke's theorem for modular group algebras: The commutative case

The Loewy and socle structure of the projective indecomposable modules for the group algebras of the Mathieu group M 12 and its automorphism group M 12.2 over an algebraically closed field of characteristic 3 are determined without using computers.

On monomial codes in modular group algebras

Modular group algebras with centrally metabelian unit groups

In this paper, we classify the modular group algebra [Formula: see text] of a group [Formula: see text] over a field [Formula: see text] of characteristic [Formula: see text] having upper Lie nilpotency index [Formula: see text] for [Formula: see text] and [Formula: see text]. Group algebras of upper Lie nilpotency index [Formula: see text] for [Formula: see text], have already been characterized completely.

We build the wrapped Fukaya category W(E) for any monotone symplectic manifold, convex at infinity. We define the open-closed and closed open-string maps. We study their algebraic properties and prove that the string maps are compatible with the eigenvalue splitting of W(E). We extend Abouzaid's generation criterion from the exact to the monotone setting. We construct an acceleration functor from the compact Fukaya category which on Hochschild (co)homology commutes with the string maps and the canonical map from quantum cohomology QH(E) to symplectic cohomology SH(E). We define the QH(E)- and SH(E)-module structure on the Hochschild (co)homology of W(E) which is compatible with the string maps. The module and unital algebra structures, and the generation criterion, also hold for the compact Fukaya category F(E), and also hold for closed monotone symplectic manifolds. As an application, we show that the wrapped category of any monotone negative line bundle over any projective space is proper (cohomologically finite). For any monotone negative line bundle E over a toric Fano variety, we show that SH(E) is non-trivial and that W(E) contains an essential non-displaceable monotone Lagrangian torus.

A new canonical induction formula for p-permutation modules

Sections and Irreducible Modules

We construct a pair of adjoint functors between the categories of crossed modules of groups and associative algebras and establish an equivalence of categories between module structures over a crossed module of groups and its respective crossed module of associative algebras.

Let p be a prime, R a commutative ring of characteristic p , G a p -primary abelian group, and V(RG) the group of normalized units in the group algebra RG . It is largely determined when V(RG) is totally projective. This generalizes the well-known special case when R is a perfect field. Moreover, the current proof has the advantage of greater clarity.

This paper presents the socle series of the projective indecomposable modules for the triple cover 3 ^ M 22 \hat 3{M_{22}} in characteristic 2. The results are obtained by computational means; the methods as well as the constructive approach are explained.

Ehresmann semigroups whose categories are EI and their representation theory

Undergraduate Biomedical Science dissertations are the culmination of a student’s academic journey and allow students to refine technical proficiencies, experimental design and data analysis. However, traditional dissertation projects may not fully meet the requirements of diverse student populations and employer’s needs. This research project aims to assess the effectiveness of modifying the assessment format for final-year projects, incorporating elements such as lay summaries, project proposals, scientific research papers, and oral poster defences. The objective was to cultivate higher-order critical thinking skills and enhance written and verbal communication competencies, in addition to developing a suite of transferable skills which are highly sought by employers. Quantitative data were primarily generated via end-of-module feedback reports and the module satisfaction survey. Students rated their confidence in a suite of transferable skills pre and post-completion of the project module using a four-point Likert scale. Staff perceptions (n = 30) and module board reports were also evaluated. For all data, a paired t-test for related groups was conducted. Thematic analysis was used to analyse qualitative data using the Braun and Clark Framework. The end-of-module feedback was overwhelmingly positive with all students agreeing that they were satisfied with the module. Students reported a statistically significant increase in confidence within 11 transferable skills which are considered core within the industry, for example, critical thinking, problem-solving and time management. Furthermore, the mean module mark increased following the module redesign from 66.3% ± 0.2% in 2019 to 70.9% ± 0.6% in 2020 (p ≤ 0.05). Staff provided free text comments, reporting an overall improvement in the module, a reduction in workload and a better teaching experience. Students exhibited appreciation of the new module structure, assessment suit and creative liberty within the projects. The redesigned project module enhanced the teaching experience for staff, whilst students appreciated the diverse range of projects and assessments that featured shorter word limits and a creative flair. Universities must reinvent undergraduate dissertations to equip students with essential employability skills.

For modular abelian group algebras over a perfect field of prime characteristic, a connection is given between the direct factor problem and the isomorphism problem.

Ribbon tensor structure on the full representation categories of the singlet vertex algebras