2-上循环交叉积

2-Cocycle crossed products

导出

摘要利用von Neumann代数M和带有正规的2-上循环μ的离散群G,定义了2-上循环交叉积,推广了经典的离散交叉积,并证明了2-上循环交叉积具有结合律. A 2-cocycle crossed product is defined in this paper given avon Neumann algebra ~4 and a discrete group G with a normalized 2-cocycle μ on it, which generalizes the classical discrete crossed product. Also, the associative law of the 2-cocycle crossed product is shown in this paper.

作者赵建伟

机构地区中国计量学院理学院数学系

出处《中国科学：数学》 CSCD 北大核心 2011年第3期271-278,共8页 Scientia Sinica：Mathematica

基金国家自然科学基金(批准号:10926118) 浙江省自然科学基金(批准号:Y6110117)资助项目

关键词 yon NEUMANN 代数2-上循环交叉积结合律 von Neumann algebra, 2-cocycle crossed product, associative law

分类号 O152.5 [理学—基础数学]

引文网络
相关文献

参考文献14

1Murray F J, von Neumann J. On rings of operators. Ann Math, 1936, 37:116-229.
2Murray F J, von Neumann J. On rings of operators IV. Ann Math, 1943, 44:716-808.
3Voiculescu D, Dykema K, Nica A. Free Random Variable. CRM Monogr Ser, vol. 1. Providence, RI: Amer Math Soc, 1992.
4Popa S. On Ozawa's property for free group factors. Int Math Res Notices, 2007, doi:10.1093/imrn/rnm036.
5Vaes S. An inner amenable group whose von Neumann algebra does not have property Gamma. arXiv: 0909.1485, 2009.
6Ioana A, Popa S, Vaes S. A class of superrigid group yon Neumann algebras, arXiv: 1007.1412vl, 2010.
7Connes A, Jones V F R. Property (T) for von Neumann algebras. Bull London Math Soc, 1985, 17:5742.
8Nicoara R, Popa S, Sasyk R. On II1 factors arising from 2-cocycles of w-rigid groups. J Funct Anal, 2007, 242:230-246.
9Turumaru T. Crossed products of operator algebras. Tohoku Math J, 1958, 10:335-365.
10Nakamura M, Takeda Z. On some elementary properties of the crossed product of von Neumann algebras. Proc Japan Acad Ser A Math Sci, 1958, 34:489-494.

二级参考文献36

1Woronowicz S L. Twisted SU(2) group, an example of a non-commutative differential calculus. Publ RIMS, Kyoto, 1987, 23:117-181.
2Lance E C. An explicit description of the fundamental unitary for SUp (2). Commun Math Phys, 1994,164:1-15.
3Woronowicz S L. Quantum SU(2) and E(2) groups, contraction procedure. Commun Math Phys, 1992,149:635-652.
4Tomiyama J. Invitation to C^*-Algebras and Topological Dynamics. Singapore: World Scientific, 1987.
5Fillmore A. A User's Guide to Oerator Algebras. Canadian Mathematical Society Series of Monographs and Advanced Texts (A Wiley-Interscience Publication). New York: John Wiley & Sons. Inc. 1996.
6Van Daele A. The Haar measure on a Woronowicz C^*-algebra. Proc Amer Math Soc, 1995, 123(10):3125-3128.
7Podles P. Symmetries of quantum spaces, subgroups and quotient spaces of quantum SU(2) and SO(3) groups. Commun Math Phys, 1995, 170:1-20.
8Wang Shuzhou. Free products of Woronowicz C^*-algebras. Commun Math Phys, 1995, 167:671-692.
9Wang Shuzhou. Tensor products and crossed products of Woronowicz C^*-algebras. Proc London Math Soc, 1995, 71(3): 695-720.
10Sunder V S. An Invitation to von Neumann Algebras. New York: Springer-Verlag, World Publishing Corporation, 1987.

1陈本菊,向玉玲,严倩.C*代数的离散交叉积[J].宜宾学院学报,2015,15(12):95-97.
2杜宁,吉国兴.von Neumann代数上保持半*-Jordan积的映射[J].纺织高校基础科学学报,2013,26(2):203-207. 被引量：2
3赵建伟.一列非同构的离散交叉积(英文)[J].数学杂志,2011,31(2):263-270.
4赵建伟.作用在n维欧氏空间R^n上的离散交叉积[J].数学学报（中文版）,2008,51(3):607-616.
5张建华,杜鸿科.von Neumann代数中套子代数的摄动[J].数学学报（中文版）,2002,45(1):197-202.
6朱军,熊昌萍.环上的广义导子与Von Neumann代数上的P-核值保持映射[J].数学学报（中文版）,1998,41(4):795-800. 被引量：19
7ErikCHRISTENSEN.On Some Problems Studied by R. V. Kadison[J].Acta Mathematica Sinica,English Series,2003,19(3):523-534.
8赵连阔,侯晋川.算子代数上保零积的可加映射(英文)[J].山西师范大学学报（自然科学版）,2004,18(4):21-25.
9李怡铮,侯成军.群射影酉表示的von Neumann代数[J].曲阜师范大学学报（自然科学版）,2011,37(4):37-40.
10WeiGUO.Unitary Bases and Noncommutative Wavelets[J].Acta Mathematica Sinica,English Series,2003,19(3):591-594. 被引量：4

中国科学：数学

2011年第3期

浏览历史

内容加载中请稍等...

2-上循环交叉积

参考文献14

二级参考文献36

相关作者

相关机构

相关主题

浏览历史