Geodesic
HOMOLOGICAL DIMENSIONS OF CROSSED PRODUCTS
Glasgow mathematical journal, Tome 59 (2017) no. 2, pp. 401-420

Voir la notice de l'article provenant de la source Cambridge University Press

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 αG are classified: global dimension of A σ αG is either infinity or equal to that of A, and finitistic dimension of Aσ αG 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 ≤ G, we show that A and Aα σ G share the same homological dimensions under extra assumptions, extending the main results in (Li, Representations of modular skew group algebras, Trans. Amer. Math. Soc.367(9) (2015), 6293–6314, Li, Finitistic dimensions and picewise hereditary property of skew group algebras, to Glasgow Math. J.57(3) (2015), 509–517). 
LI, LIPING. HOMOLOGICAL DIMENSIONS OF CROSSED PRODUCTS. Glasgow mathematical journal, Tome 59 (2017) no. 2, pp. 401-420. doi: 10.1017/S0017089516000240
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