2025/12/10 by Weikang Weng, Weng, Weikang
Mathematics · #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #Advanced Combinatorial Mathematics
paper · pdf · doi:10.48550/arxiv.2512.09692
In this paper, we construct recollements and ladders for Brieskorn-Pham singularities via reduction/insertion functors, and study the singularity categories of the Brieskorn-Pham singularities using these ladders. In particular, we construct a class of tilting objects, called the extended tilting n-cuboids, whose endomorphism algebras are n-fold tensor products of certain Nakayama algebras. Moreover, we show that such an endomorphism algebra is derived equivalent to a certain replicated algebra. This generalizes the Happel-Seidel symmetry to the context of Brieskorn-Pham singularities.