几类交叉余积的关系

数学物理学报 ›› 2011, Vol. 31 ›› Issue (1): 117-131.

几类交叉余积的关系

方小利^1,2|李金其³

1.绍兴文理学院数理信息学院浙江绍兴 312000|2.东南大学数学系南京 210096; 3.浙江师范大学数理信息学院浙江金华 321004

收稿日期:2008-10-08 修回日期:2009-08-06 出版日期:2011-02-25 发布日期:2011-02-25
基金资助:
国家自然科学基金(10971188)、江苏博士后基金(0902081C)和浙江省教育厅基金(Y200907995)资助

Relations with All Kinds of Crossed Coproducts

FANG Xiao-Li^1,2, LI Jin-Ji³

1.Department of Mathematics, Shaoxing College of Arts and Sciences, Zhejiang Shaoxing 312000|2.Department of Mathematics, Southeast University, Nanjing 210096|3.College of Mathematics and Physics, Zhejiang Normal University, Zhejiang Jinhua 321004

Received:2008-10-08 Revised:2009-08-06 Online:2011-02-25 Published:2011-02-25
Supported by:
国家自然科学基金(10971188)、江苏博士后基金(0902081C)和浙江省教育厅基金(Y200907995)资助

摘要/Abstract

摘要：

该文引进了广义对角交叉余积, 广义 L-R smash 余积, 广义双边交叉余积和双边smash余积并研究它们的关系. 特别地, 给出了两种不同方法来解释广义对角交叉余积与广义L-R smash 余积之间的关系. 作为应用, 运用比较简单的证明给出关于iterated广义smash余积的一个重要的结论.

关键词: 广义对角交叉余积, 广义L-R smash 余积, 双边交叉余积, L-R扭曲余组

Abstract:

The so-called generalized diagonal crossed coproduct, generalized L-R smash coproduct, generalized two-sided crossed coproduct and two-sided smash coproduct are introduced and their relations are investigated. In particular, the authors give two different interpretations about relations between generalized diagonal crossed coproducts and generalized L-R smash coproducts. As an application, an easy conceptual proof of an important but very technical result concerning iterated generalized smash coproducts is obtained.

Key words: Generalized diagonal crossed coproducts, Generalized L-R smash coproducts, Two-sided crossed coproducts, L-R twisting codatum

中图分类号:

16W30

方小利, 李金其. 几类交叉余积的关系[J]. 数学物理学报, 2011, 31(1): 117-131.

FANG Xiao-Li, LI Jin-Ji. Relations with All Kinds of Crossed Coproducts[J]. Acta mathematica scientia,Series A, 2011, 31(1): 117-131.

参考文献

[1] Bieliavsky P, Bonneau P, Maeda Y. Universal deformation formulae, symplectic Lie groups and symmetric spaces. Pacific Journal of Mathematics, 2007, 230: 41--58

[2] Bieliavsky P, Bonneau P, Maeda Y. Universal Deformation Formulae for Three-dimensional Solvable Lie Groups. Quantum Field Theory and Noncommutative Geometry. Berlin, New York: Springer, 2005: 127--138

[3] Bonneau P, Gerstenhaber M, Giaquinto A, Sternheimer D. Quantum groups and deformation quantization: explicit approaches and implicit aspects. J Math Phys, 2004, 45: 3703--3741

[4] Bonneau P, Sternheimer D. Topological Hopf Algebras Quantum Groups and Deformation Quantization. Lecture Notes in Pure and appl Math. New York: Marcel Dekker, 2005: 55--70

[5] Bulacu D, Panaite F, Oystaeyen F V. Generalized diagonal crossed products and smash products for quasi-Hopf algebras
applications. Comm Math Phys, 2006, 266: 355--399

[6]} Ferrer Santos W R, Torrecillas B. Twisting products in algebras II. K-Theory, 1999, 17: 37--53

[7] Hausser F, Nill F. Diagonal crossed products by duals of quasi-quantum groups. Rev Math Phys, 1999, 11: 553--629

[8] Kassel C. Quantum Groups. Graduate Texts in Mathematics 155. Berlin: Springer, 1995

[9] Majid S. Foundations of Quantum Group Theory. Cambridge: Cambridge Univ Press, 1995

[10] Montgomery S. Hopf Algebras and Their Actions on Rings. CBMS Lecture Notes. Providence, RI: AMS, 1993

[11] Panaite F, Oystaeyen F V. L-R-smash product for (quasi) Hopf algebras. J Algebra, 2007, 309: 168--191

[12] Sweedler M E. Hopf Algebras. New York: Benjamin, 1969

[13] Wang S H, Li J Q. On twisted smash products for bimodule algebras and the Drinfeld double. Comm Algebra, 1998, 26: 2435--2444

[14] Zhao W Z, Wang S H, Jiao Z M. The twisted coproduct of the Hopf algebra and the H^R Hopf algebras. Acta Mathematica Sinica (in Chinese), 1997, 40: 591--596

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