2015/07/15 by Lluís Puig, Lluis Puig, Puig, Lluis
Mathematics · #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.GR
paper · pdf · doi:10.48550/arxiv.1507.04278
This paper precises and generalizes the previous preprint "Affirmative answer to a question of Linckelmann"
openalex publication_date 2015/07/15 · arxiv created 2021/09/29 · arxiv updated 2021/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 P-category F(b,G) associated with a block b of defect group P of a finite group G, which would include, as k*-automorphism groups of the objects, the k*-groups associated with the automizers of the corresponding selfcentralizing Brauer (b,G)-pairs, introduced in [3, 6.6]; as a matter of fact, in this question the selfcentralizing Brauer pairs can be replaced by the nilcentralized Brauer pairs, still getting a positive answer. But the condition on the k*-automorphism groups of the objects is not precise enough to guarantee the uniqueness of a solution, as showed by Sejong Park in [2, Theorem 1.3]. This uniqueness depends on the folder structure [5,~Section~2] associated with F(b,G) in [4,~Theorem~11.32], and here we prove the existence and the uniqueness of such a regular central k*-extension for any folded Frobenius P-category.