Let L/F be a finite Galois extension of number fields of degree n and let p be a prime which does not divide n.We shall study the p^(j)-rank of K_(2i)(O_(L))via its Galois module structure following the approaches of ...Let L/F be a finite Galois extension of number fields of degree n and let p be a prime which does not divide n.We shall study the p^(j)-rank of K_(2i)(O_(L))via its Galois module structure following the approaches of Iwasawa and Komatsu–Nakano.Along the way,we generalize previous observations of Browkin,Wu and Zhou on K_(2)-groups to higher even K-groups.We also give examples to illustrate our results.Finally,we apply our discussion to refine a result of Kitajima pertaining to the p-rank of even K-groups in the cyclotomic Z_(l)-extension,where l≠p.展开更多
We obtain the K-groups of the operator ideals contained in the class of Riesz operators. And based on the results, we calculate the K-groups of the operator algebras on HD nspaces and QDn spaces.
In this paper we discuss the K-groups of Wiener algebra ;W. For the 1-shift space XGM2,We obtain a characterization of Fredholm operators on X^nGM2 for all n ∈ N. We also calculate the K-groups of operator algebra on...In this paper we discuss the K-groups of Wiener algebra ;W. For the 1-shift space XGM2,We obtain a characterization of Fredholm operators on X^nGM2 for all n ∈ N. We also calculate the K-groups of operator algebra on the 1-shift space XGM2.展开更多
In the present paper, it is proved that the K0-group of a Toeplitz algebra on any connected domain is always isomorphic to the K0-group of the relative continuous function algebra. In addition, the cohomotopy groups o...In the present paper, it is proved that the K0-group of a Toeplitz algebra on any connected domain is always isomorphic to the K0-group of the relative continuous function algebra. In addition, the cohomotopy groups of essential boundaries of some connected domains are computed, and the K0-groups of the continuous function algebras on these domains are also computed.展开更多
In this paper we show that the Fibered Isomorphism Conjecture of Farrell and Jones, corresponding to the stable topological pseudoisotopy functor, is true for the fundamental groups of a class of complex manifolds. A ...In this paper we show that the Fibered Isomorphism Conjecture of Farrell and Jones, corresponding to the stable topological pseudoisotopy functor, is true for the fundamental groups of a class of complex manifolds. A consequence of this result is that the Whitehead group, reduced projective class groups and the negative K-groups of the fundamental groups of these manifolds vanish whenever the fundamental group is torsion free. We also prove the same results for a class of real manifolds including a large class of 3-manifolds which has a finite sheeted cover fibering over the circle.展开更多
Suppose A is a unital C＊-algebra and r 1.In this paper,we define a unital C＊-algebra C（cb）＊（A,r） and a completely bounded unital homomorphism αr：A → C（cb）＊（A,r）with the property that C（cb）＊（A,r）=C...Suppose A is a unital C＊-algebra and r 1.In this paper,we define a unital C＊-algebra C（cb）＊（A,r） and a completely bounded unital homomorphism αr：A → C（cb）＊（A,r）with the property that C（cb）＊（A,r）=C＊（αr（A））and,for every unital C＊-algebra B and every unital completely bounded homomorphism φ：A→ B,there is a（unique）unital ＊-homomorphism π：C（cb）＊（A,r）→B such thatφ=πoαr.We prove that,if A is generated by a normal set {tλ：λ∈Λ},then C（cb）＊（A,r）is generated by the set {αr（tλ）：λ∈Λ}.By proving an equation of the norms of elements in a dense subset of C（cb）＊（A,r）we obtain that,if Β is a unital C＊-algebra that can be embedded into A,then C（cb）＊（B,r）can be naturally embedded into C（cb）＊（A,r）.We give characterizations of C（cb）＊（A,r）for some special situations and we conclude that C（cb）＊（A,r）will be ＂nice＂ when dim（A）≤ 2 and ＂quite complicated＂ when dim（A）≥ 3.We give a characterization of the relation between K-groups of A and K-groups of C（cb）＊（A,r）.We also define and study some analogous of C（cb）＊（A,r）.展开更多
Some basic questions on ultraproducts of C~*-algebras and von Neumann al- gebras,including the relation to K-theory of C~*-algebras are considered.More specifically, we prove that under certain conditions,the K-groups...Some basic questions on ultraproducts of C~*-algebras and von Neumann al- gebras,including the relation to K-theory of C~*-algebras are considered.More specifically, we prove that under certain conditions,the K-groups of ultraproduct of C~*-algebras are iso- morphic to the ultraproduct of respective K-groups of C~*-algebras.We also show that the ultraproducts of factors of type Ⅱ_1 are prime,i.e.not isomorphic to any non-trivial tensor product.展开更多
基金Supported by National Natural Science Foundation of China(Grant No.11771164)the Fundamental Research Funds for the Central Universities of CCNU(Grant No.CCNU20TD002)。
文摘Let L/F be a finite Galois extension of number fields of degree n and let p be a prime which does not divide n.We shall study the p^(j)-rank of K_(2i)(O_(L))via its Galois module structure following the approaches of Iwasawa and Komatsu–Nakano.Along the way,we generalize previous observations of Browkin,Wu and Zhou on K_(2)-groups to higher even K-groups.We also give examples to illustrate our results.Finally,we apply our discussion to refine a result of Kitajima pertaining to the p-rank of even K-groups in the cyclotomic Z_(l)-extension,where l≠p.
基金Supported by National Natural Science Foundation of China (Grant Nos. 10926173 and 10771034)Natural Science Foundation of Fujian Province of China (Grant No. 2009J05002)Foundation of Technology and Development of Fuzhou University (Grant No. 2007-XY-11)
文摘We obtain the K-groups of the operator ideals contained in the class of Riesz operators. And based on the results, we calculate the K-groups of the operator algebras on HD nspaces and QDn spaces.
基金National Natural Science Foundation of China (10471025,10771034)National Natural Science Foundation of Fujian Province (S0650009)Foudation of the Education Department of Fujian Provience (JA04170,JB07047)
文摘In this paper we discuss the K-groups of Wiener algebra ;W. For the 1-shift space XGM2,We obtain a characterization of Fredholm operators on X^nGM2 for all n ∈ N. We also calculate the K-groups of operator algebra on the 1-shift space XGM2.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 10371082)
文摘In the present paper, it is proved that the K0-group of a Toeplitz algebra on any connected domain is always isomorphic to the K0-group of the relative continuous function algebra. In addition, the cohomotopy groups of essential boundaries of some connected domains are computed, and the K0-groups of the continuous function algebras on these domains are also computed.
文摘In this paper we show that the Fibered Isomorphism Conjecture of Farrell and Jones, corresponding to the stable topological pseudoisotopy functor, is true for the fundamental groups of a class of complex manifolds. A consequence of this result is that the Whitehead group, reduced projective class groups and the negative K-groups of the fundamental groups of these manifolds vanish whenever the fundamental group is torsion free. We also prove the same results for a class of real manifolds including a large class of 3-manifolds which has a finite sheeted cover fibering over the circle.
基金partially supported by a Collaboration Grant from the Simons Foundation
文摘Suppose A is a unital C＊-algebra and r 1.In this paper,we define a unital C＊-algebra C（cb）＊（A,r） and a completely bounded unital homomorphism αr：A → C（cb）＊（A,r）with the property that C（cb）＊（A,r）=C＊（αr（A））and,for every unital C＊-algebra B and every unital completely bounded homomorphism φ：A→ B,there is a（unique）unital ＊-homomorphism π：C（cb）＊（A,r）→B such thatφ=πoαr.We prove that,if A is generated by a normal set {tλ：λ∈Λ},then C（cb）＊（A,r）is generated by the set {αr（tλ）：λ∈Λ}.By proving an equation of the norms of elements in a dense subset of C（cb）＊（A,r）we obtain that,if Β is a unital C＊-algebra that can be embedded into A,then C（cb）＊（B,r）can be naturally embedded into C（cb）＊（A,r）.We give characterizations of C（cb）＊（A,r）for some special situations and we conclude that C（cb）＊（A,r）will be ＂nice＂ when dim（A）≤ 2 and ＂quite complicated＂ when dim（A）≥ 3.We give a characterization of the relation between K-groups of A and K-groups of C（cb）＊（A,r）.We also define and study some analogous of C（cb）＊（A,r）.
基金supported by the National Natural Science Foundation of China(Grant No.10471137).
文摘Some basic questions on ultraproducts of C~*-algebras and von Neumann al- gebras,including the relation to K-theory of C~*-algebras are considered.More specifically, we prove that under certain conditions,the K-groups of ultraproduct of C~*-algebras are iso- morphic to the ultraproduct of respective K-groups of C~*-algebras.We also show that the ultraproducts of factors of type Ⅱ_1 are prime,i.e.not isomorphic to any non-trivial tensor product.
