Notice
Tobias Moede - Coclass theory for nilpotent associative algebras
- document 1 document 2 document 3
- niveau 1 niveau 2 niveau 3
Descriptif
The coclass of a finite p-group of order p^n and class c is defined as n-c. Using coclass as the primary invariant in the investigation of finite p-groups turned out to be a very fruitful approach. Together with Bettina Eick, we have developed a coclass theory for nilpotent associative algebras over fields. A central tool are the coclass graphs associated with the algebras of a fixed coclass. The graphs for coclass zero are well understood. We give a full description for coclass one and explore graphs for higher coclasses. We prove several structural results for coclass graphs, which yield results in the flavor of the coclass theorems for finite p-groups. The most striking observation in our experimental data is that for finite fields all of these graphs seem to exhibit a periodic pattern. A similar periodicity in the graphs for finite p-groups has been proved independently by du Sautoy using the theory of zeta functions and by Eick & Leedham-Green using cohomological methods. We give an outlook on how a proof might proceed and how the periodicity may be exploited to describe the infinitely many nilpotent associative F-algebras of a fixed coclass by a finite set of data.
Thème
Sur le même thème
-
Aurel PAGE - Cohomology of arithmetic groups and number theory: geometric, asymptotic and computati…
PageAurel regisIn this lecture series, the first part will be dedicated to cohomology of arithmetic groups of lower ranks (e.g., Bianchi groups), their associated geometric models (mainly from hyperbolic geometry)
-
Phong NGUYEN - Recent progress on lattices's computations 2
NguyenPhong Q.This is an introduction to the mysterious world of lattice algorithms, which have found many applications in computer science, notably in cryptography. We will explain how lattices are represented by
-
Oussama Hamza - Hilbert series and mild groups
Let $p$ be an odd prime number and $G$ a finitely generated pro-$p$ group. Define $I(G)$ the augmentation ideal of the group algebra of $G$ over $F_p$ and define the Hilbert series of $G$ by: $G(t):
-
Alexander HULPKE - Computational group theory, cohomology of groups and topological methods 4
The lecture series will give an introduction to the computer algebra system GAP, focussing on calculations involving cohomology. We will describe the mathematics underlying the algorithms, and how to
-
Alexander HULPKE - Computational group theory, cohomology of groups and topological methods 5
The lecture series will give an introduction to the computer algebra system GAP, focussing on calculations involving cohomology. We will describe the mathematics underlying the algorithms, and how to
-
Zachary Himes - On not the rational dualizing module for $\text{Aut}(F_n)$
Bestvina--Feighn proved that $\text{Aut}(F_n)$ is a rational duality group, i.e. there is a $\mathbb{Q}[\text{Aut}(F_n)]$-module, called the rational dualizing module, and a form of Poincar\'e duality
-
Gabriele NEBE - Lattices, Perfects lattices, Voronoi reduction theory, modular forms, computations …
NebeGabrieleThe talks of Coulangeon will introduce the notion of perfect, eutactic and extreme lattices and the Voronoi's algorithm to enumerate perfect lattices (both Eulcidean and Hermitian). The talk of Nebe
-
Alexandre Booms : « Usage de matériel pédagogique adapté en géométrie : une transposition à interro…
« Usage de matériel pédagogique adapté en géométrie : une transposition à interroger ». Alexandre Booms, doctorant (Université de Reims Champagne-Ardenne - Cérep UR 4692)
-
Paul GUNNELLS - Cohomology of arithmetic groups and number theory: geometric, asymptotic and comput…
GunnellsPaul E.In this lecture series, the first part will be dedicated to cohomology of arithmetic groups of lower ranks (e.g., Bianchi groups), their associated geometric models (mainly from hyperbolic geometry)
-
Paul GUNNELLS - Cohomology of arithmetic groups and number theory: geometric, asymptotic and comput…
GunnellsPaul E.In this lecture series, the first part will be dedicated to cohomology of arithmetic groups of lower ranks (e.g., Bianchi groups), their associated geometric models (mainly from hyperbolic geometry)
-
Paul GUNNELLS - Cohomology of arithmetic groups and number theory: geometric, asymptotic and comput…
GunnellsPaul E.In this lecture series, the first part will be dedicated to cohomology of arithmetic groups of lower ranks (e.g., Bianchi groups), their associated geometric models (mainly from hyperbolic geometry)
-
Graham ELLIS - Computational group theory, cohomology of groups and topological methods 3
EllisGrahamThe lecture series will give an introduction to the computer algebra system GAP, focussing on calculations involving cohomology. We will describe the mathematics underlying the algorithms, and how to
