Let （K, O, k） be a p-modular system and G be a finite group. We prove that block A of RG and block B of RH are nalurally Morita equivalent of degree n if and only if A≌B＋…＋B}→n^2 as right R[H×H]-modules an...Let （K, O, k） be a p-modular system and G be a finite group. We prove that block A of RG and block B of RH are nalurally Morita equivalent of degree n if and only if A≌B＋…＋B}→n^2 as right R[H×H]-modules and A and B have the same defect（where R∈{k,O}）, which is a generalization of the result of Külshammer Burkhard in a p-modular system for an arbitrary subgroup H of G. It is proved that naturally Morita equivalent blocks are equivalent blocks and Morita equivalent via a bimodule with trivial source.展开更多
Let G and Gt be two finite groups, and p be a prime number, k is an algebraically closed field of characteristic p. We denote by b and b~ the block idempotents of G and Gt over k, respectively. We assume that the bloc...Let G and Gt be two finite groups, and p be a prime number, k is an algebraically closed field of characteristic p. We denote by b and b~ the block idempotents of G and Gt over k, respectively. We assume that the block algebras kGb and kG＇b＇ are basically Morita equivalent. Puig and Zhou （2007） proved that the corresponding block algebras of some special subgroups of G and G＇ are also basically Morita equivalent. We investigate the relationships between the basic Morita equivalences of two kinds of subgroups of G and G＇： We find a module such that its induced module and its restricted module induce the basic Morita equivalences respectively, hence give a precise description of these basic Morita equivalences.展开更多
基金Supported by the National Programfor the BasicScience Researches of China(G19990751)
文摘Let （K, O, k） be a p-modular system and G be a finite group. We prove that block A of RG and block B of RH are nalurally Morita equivalent of degree n if and only if A≌B＋…＋B}→n^2 as right R[H×H]-modules and A and B have the same defect（where R∈{k,O}）, which is a generalization of the result of Külshammer Burkhard in a p-modular system for an arbitrary subgroup H of G. It is proved that naturally Morita equivalent blocks are equivalent blocks and Morita equivalent via a bimodule with trivial source.
文摘Let G and Gt be two finite groups, and p be a prime number, k is an algebraically closed field of characteristic p. We denote by b and b~ the block idempotents of G and Gt over k, respectively. We assume that the block algebras kGb and kG＇b＇ are basically Morita equivalent. Puig and Zhou （2007） proved that the corresponding block algebras of some special subgroups of G and G＇ are also basically Morita equivalent. We investigate the relationships between the basic Morita equivalences of two kinds of subgroups of G and G＇： We find a module such that its induced module and its restricted module induce the basic Morita equivalences respectively, hence give a precise description of these basic Morita equivalences.
