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  • 标题:Property Γ factors and the Hochschild cohomology problem
  • 本地全文:下载
  • 作者:Erik Christensen ; Florin Pop ; Allan M. Sinclair
  • 期刊名称:Proceedings of the National Academy of Sciences
  • 印刷版ISSN:0027-8424
  • 电子版ISSN:1091-6490
  • 出版年度:2003
  • 卷号:100
  • 期号:7
  • 页码:3865-3869
  • DOI:10.1073/pnas.0737489100
  • 语种:English
  • 出版社:The National Academy of Sciences of the United States of America
  • 摘要:The main result of this article is that the kth continuous Hochschild cohomology groups Hk([M], [M]) and Hk([M], B(H)) of a von Neumann factor [M] {subseteq} B(H) of type II1 with property {Gamma} are 0 for all positive integers k. The method of proof involves the construction of hyperfinite subfactors with special properties and a new inequality of Grothendieck type for multilinear maps. We prove joint continuity in the ||*||2 norm of separately ultraweakly continuous multilinear maps and combine these results to reduce to the case of completely bounded cohomology, which is already solved.
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