The generalized noncommutative torus Tkp of rank n was defined in [4] by the crossed product Am/k ×a3 Z ×a4 … ×an Z, where the actions ai of Z on the fibre Mk(C) of a rational rotation algebra Am/k are...The generalized noncommutative torus Tkp of rank n was defined in [4] by the crossed product Am/k ×a3 Z ×a4 … ×an Z, where the actions ai of Z on the fibre Mk(C) of a rational rotation algebra Am/k are trivial, and C*(kZ × kZ) ×a3 Z ×a4 ... ×an Z is a completely irrational noncommutative torus Ap of rank n. It is shown in this paper that Tkp is strongly Morita equivalent to Ap, and that Tkp (?) Mp∞ is isomorphic to Ap (?) Mk(C) (?) Mp∞ if and only if the set of prime factors of k is a subset of the set of prime factors of p.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Project supported by Grant No.1999-2-102-001-3 from the Interdisciplinary Research Program Year of the KOSEF.
文摘The generalized noncommutative torus Tkp of rank n was defined in [4] by the crossed product Am/k ×a3 Z ×a4 … ×an Z, where the actions ai of Z on the fibre Mk(C) of a rational rotation algebra Am/k are trivial, and C*(kZ × kZ) ×a3 Z ×a4 ... ×an Z is a completely irrational noncommutative torus Ap of rank n. It is shown in this paper that Tkp is strongly Morita equivalent to Ap, and that Tkp (?) Mp∞ is isomorphic to Ap (?) Mk(C) (?) Mp∞ if and only if the set of prime factors of k is a subset of the set of prime factors of p.
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.
