摘要:

A sufficient condition is given such that the curves ΓD:x4$y4=Dz4have no points in any odd‐degree (greater than 1) extension field of the rationals. The condition is in terms of the rational rank of an elliptic curve in the Jacobian of ΓD. Various examples are given.

ISSN:0024-6115    

DOI:10.1112/plms/s3-52.2.193

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6115    

DOI:10.1112/plms/s3-52.2.215

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6115    

DOI:10.1112/plms/s3-52.2.236

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6115    

DOI:10.1112/plms/s3-52.2.269

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6115    

DOI:10.1112/plms/s3-52.2.305

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6115    

DOI:10.1112/plms/s3-52.2.328

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6115    

DOI:10.1112/plms/s3-52.2.349

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

Let τ be an action of a compact Lie groupGon an unital C*‐algebraA, and letAFbe theG‐finite elements inA. We show that if τ satisfies a certain spectral condition, then any*‐derivation δ defined onAF, and mappingAF, is closable and its closure generates a one‐parameter group of*‐automorphisms. The condition on τ is fulfilled in the cases where τ has full spectrum, or ifAseparating family ï ∈Ĝis associated with Hilbert spaces inAin the sense of Roberts, or ifGis abelian and the condition Γ of [7] is fulfilled. The proof is based on an argument of K. Thomsen, who proved the theorem in the case whereGis abelian [25]. A more detailed study is made of the cononical action ofG=U(n)on the Cuntz's algebraCn, and, in particular, we find that any derivation onAFvanshing on the fixed point algebra for this action is the generator of a one‐parameter subgroup fo the action.

ISSN:0024-6115    

DOI:10.1112/plms/s3-52.2.369

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6115    

DOI:10.1112/j.1460-244X.1986.tb00434.x

出版商:Oxford University Press    

年代:1986

数据来源: WILEY