Existence, uniqueness and functoriality of the perfect locality over a Frobenius P-category

@article{Puig2012ExistenceUA,
  title={Existence, uniqueness and functoriality of the perfect locality over a Frobenius P-category},
  author={Lluis Puig},
  journal={arXiv: Group Theory},
  year={2012}
}
  • L. Puig
  • Published 30 June 2012
  • Mathematics
  • arXiv: Group Theory
Let p be a prime, P a finite p-group and F a Frobenius P-category. The question on the existence of a suitable category Lsc extending the full subcategory of F over the set of F-selfcentralizing subgroups of P goes back to Dave Benson in 1994. In 2002 Carles Broto, Ran Levi and Bob Oliver formulate the existence and the uniqueness of the category Lsc in terms of the annulation of an obstruction 3-cohomology element and of the vanishing of a 2-cohomology group, and they state a sufficient… 
5 Citations
Note on the universality and the functoriality of the perfect F-locality
In "Frobenius Categories versus Brauer Blocks" we have proved some universality of the so-called localizing functor associated with a Frobenius $P$-category $F$, where $P$ is a finite $p$-group, with
A Correction to the Uniqueness of a Partial Perfect Locality over a Frobenius P-Category
Let $p$ be a prime, $P$ a finite p-group and $\cal F$ a Frobenius $P$-category. In "Existence, uniqueness and functoriality of the perfect locality over a Frobenius $P$-category", Algebra Colloquium,
Beyond a question of Markus Linckelmann
In the 2002 Durham Symposium, Markus Linckelmann [1] conjectured the existence of a regular central k*-extension of the full subcategory over the selfcentralizing Brauer pairs of the Frobenius
A Remark on the Construction of Centric Linking Systems
We give examples to show that it is not, in general, possible to prove the existence and uniqueness of centric linking systems associated to a given fusion system inductively by adding one conjugacy
A criterion on vanishing cohomology
  • 2014

References

SHOWING 1-9 OF 9 REFERENCES
The Hecke algebra of a Frobenius P-category
We introduce a new avatar of a Frobenius P-category F in the form of a suitable sub-ring H_F of the double Burnside ring of P - called the Hecke algebra of F - where we are able to formulate the
EXISTENCE AND UNIQUENESS OF LINKING SYSTEMS: CHERMAK’S PROOF VIA OBSTRUCTION THEORY
We present a version of a proof by Andy Chermak of the existence and uniqueness of centric linking systems associated to arbitrary saturated fusion systems. This proof differs from the one in [Ch] in
The homotopy theory of fusion systems
The main goal of this paper is to identify and study a certain class of spaces which in many ways behave like p-completed classifying spaces of finite groups. These spaces occur as the “classifying
Fusion systems and localities
We introduce objective partial groups, of which the linking systems and p-local finite groups of Broto, Levi, and Oliver, the transporter systems of Oliver and Ventura, and the
Structure locale dans les groupes finis
© Mémoires de la S. M. F., 1976, tous droits réservés. L’accès aux archives de la revue « Mémoires de la S. M. F. » (http:// smf.emath.fr/Publications/Memoires/Presentation.html) implique l’accord
Some remarks on vanishing cohomology
Frobenius Categories versus Brauer Blocks
Frobenius categories and localities: history and survey, Workshop “Topology, Representation theory and Cohomology
  • EPFL
  • 2005