2014/04/16 by Liping Li, Li, Liping · 1 citation
Mathematics · #16E10 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #math.GR #math.RT #msc:16E10
paper · pdf · doi:10.48550/arxiv.1404.4402
Proof simplified, typos and mistakes corrected. A big revision for induction and restriction by using theory of separable extensions
openalex publication_date 2014/04/16 · arxiv created 2014/06/13 · arxiv updated 2014/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we consider several homological dimensions of crossed products A α σ G, where A is a left Noetherian ring and G is a finite group. We revisit the induction and restriction functors in derived categories, generalizing a few classical results for separable extensions. The global dimension and finitistic dimension of A σ α G are classified: global dimension of A σ α G is either infinity or equal to that of A, and finitistic dimension of A σ α G coincides with that of A. A criterion for skew group rings to have finite global dimensions is deduced. Under the hypothesis that A is a semiprimary algebra containing a complete set of primitive orthogonal idempotents closed under the action of a Sylow p-subgroup S \leqslant G, we show that A and A α σ G share the same homological dimensions under extra assumptions, extending the main results of the author in some previous papers.