The theory of crossed products of C*-algebras by groups of automorphisms is a well-developed area of the theory of operator algebras. Given the importance and the success ofthat theory, it is natural to attempt to ext...The theory of crossed products of C*-algebras by groups of automorphisms is a well-developed area of the theory of operator algebras. Given the importance and the success ofthat theory, it is natural to attempt to extend it to a more general situation by, for example,developing a theory of crossed products of C*-algebras by semigroups of automorphisms, or evenof endomorphisms. Indeed, in recent years a number of papers have appeared that are concernedwith such non-classicaltheories of covariance algebras, see, for instance [1-3].展开更多
Let G be a second countable locally compact groupoid with Haar system {λuH}, H be aclosed subgroupoid containing G^0 with Haar system {λuH}. T.Masuda introduced the C^*-Groupoid dynamic system (G, A, α) and its red...Let G be a second countable locally compact groupoid with Haar system {λuH}, H be aclosed subgroupoid containing G^0 with Haar system {λuH}. T.Masuda introduced the C^*-Groupoid dynamic system (G, A, α) and its reduced crossed product Crea(G, A) in [2]： where A is C^*-algebra α is the komomorphism G → Aut(A). In this paper the author introduces the C^*-groupoid dynamic systems (H,A, α/H) and (H\G2,A,^-α) induced by (G,A,α) and proves that C*red(H, A) and C^*red(H\G^2, A) are strongly Morita equivalent Moreover the inducedrepresentation from C^*red(H, A) to C^*red(G,A) is got.展开更多
Let L be an n-dimensional nilpotent Lie algebra with a basis{x1…,xn),and every xi acts as a locally nilpotent derivation on algebra A. This paper shows that there exists a set of derivations{y1,…,yn}on U(L) such tha...Let L be an n-dimensional nilpotent Lie algebra with a basis{x1…,xn),and every xi acts as a locally nilpotent derivation on algebra A. This paper shows that there exists a set of derivations{y1,…,yn}on U(L) such that (A#U(L))#k{y,1,…,yn] is ismorphic to the Weyl algebra An(A).The author also uses the de4rivations to obtain a necessary and sufficient condition for a finite dimesional Lie algebra to be nilpotent.展开更多
文摘The theory of crossed products of C*-algebras by groups of automorphisms is a well-developed area of the theory of operator algebras. Given the importance and the success ofthat theory, it is natural to attempt to extend it to a more general situation by, for example,developing a theory of crossed products of C*-algebras by semigroups of automorphisms, or evenof endomorphisms. Indeed, in recent years a number of papers have appeared that are concernedwith such non-classicaltheories of covariance algebras, see, for instance [1-3].
文摘Let G be a second countable locally compact groupoid with Haar system {λuH}, H be aclosed subgroupoid containing G^0 with Haar system {λuH}. T.Masuda introduced the C^*-Groupoid dynamic system (G, A, α) and its reduced crossed product Crea(G, A) in [2]： where A is C^*-algebra α is the komomorphism G → Aut(A). In this paper the author introduces the C^*-groupoid dynamic systems (H,A, α/H) and (H\G2,A,^-α) induced by (G,A,α) and proves that C*red(H, A) and C^*red(H\G^2, A) are strongly Morita equivalent Moreover the inducedrepresentation from C^*red(H, A) to C^*red(G,A) is got.
基金Project supported by the National Natural Science Foundation of Chin
文摘Let L be an n-dimensional nilpotent Lie algebra with a basis{x1…,xn),and every xi acts as a locally nilpotent derivation on algebra A. This paper shows that there exists a set of derivations{y1,…,yn}on U(L) such that (A#U(L))#k{y,1,…,yn] is ismorphic to the Weyl algebra An(A).The author also uses the de4rivations to obtain a necessary and sufficient condition for a finite dimesional Lie algebra to be nilpotent.
