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浙江大学学报（理学版）
浙江大学学报（理学版）  2018, Vol. 45 Issue (6): 651-655,672    DOI: 10.3785/j.issn.1008-9497.2018.06.001
数学与计算机科学     
微分分次Poisson Hopf代数的张量积
胡献国, 郭梦甜, 吕家凤
浙江师范大学 数学系, 浙江 金华 321004
The tensor product of differential graded Poisson Hopf algebras
HU Xianguo, GUO Mengtian, LYU Jiafeng
Department of Mathematics, Zhejiang Normal University, Jinhua 321004, Zhejiang Province, China
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摘要： 证明了任意2个p次微分分次Poisson Hopf代数的张量积仍为p次微分分次Poisson Hopf代数.作为应用，证明了p次微分分次Poisson Hopf代数构成的范畴dg-PHA是对称monoidal范畴.
关键词： p次微分分次Poisson Hopf代数;  张量积;  对称monoidal范畴    
Abstract: This paper studies p-differential graded Poisson Hopf algebras and proves that the tensor product of p-differential graded Poisson Hopf algebras is also a p-differential graded Poisson Hopf algebra. As an application, we show that the category of p-differential graded Poisson Hopf algebras, denoted by dg-PHA, belongs to symmetric monoidal category.
Key words: p-differential graded Poisson Hopf algebras    tensor product    symmetric monoidal category
收稿日期: 2017-11-09 出版日期: 2018-11-25
CLC:  O154.2  
基金资助: 国家自然科学基金资助项目（11571316）；浙江省自然科学基金资助项目（LY16A010003）.
通讯作者: 吕家凤,ORCID:http://orcid.org/0000-0002-2637-142X,E-mail:jiafenglv@zjnu.edu.cn.     E-mail: jiafenglv@zjnu.edu.cn
作者简介: 胡献国(1992-),ORCID:http://orcid.org/0000-0002-8084-9199,男,硕士研究生,主要从事代数学研究.
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引用本文:

胡献国, 郭梦甜, 吕家凤. 微分分次Poisson Hopf代数的张量积[J]. 浙江大学学报（理学版）, 2018, 45(6): 651-655,672.

HU Xianguo, GUO Mengtian, LYU Jiafeng. The tensor product of differential graded Poisson Hopf algebras. Journal of Zhejiang University (Science Edition), 2018, 45(6): 651-655,672.

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https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2018.06.001    或    https://www.zjujournals.com/sci/CN/Y2018/V45/I6/651

[1] HUEBSCHMANN J. Poisson cohomology and quantization[J]. Journal Für Die Reine Und Angewandte Mathematik,1990, 408:57-113.
[2] XU X P. Novikov-Poisson algebras[J]. Journal of Algebra,1997, 190(2):253-279.
[3] CASAS J M,DATUASHVILI T. Noncommutative Leibniz-Poisson algebras[J]. Communications in Algebra,2006, 34(7):2507-2530.
[4] MICHELV D B. Double Poisson algebras[J]. Transactions of the American Mathematical Society, 2008, 360(11):5711-5769.
[5] DRINFEL'D V G.Quantum groups[J]. Journal of Soviet Mathematics, 1988, 41(2):898-915.
[6] LYU J F, WANG X T, ZHUANG G B. Universal enveloping algebras of Poisson Hopf algebras[J]. Journal of Algebra, 2015, 426:92-136.
[7] BECK K A, SATHER-WAGSTAFF S. A somewhat gentle introduction to differential graded commutative algebra[C]//Connections Between Algebra, Combinatorics, and Geometry Springer Proceeding in Mathematics and Statistics. New York:Springer, 2014, 76(2):3-99.
[8] FRANKILD A, JØRGENSEN P. Homological identities for differential graded algebras[J]. Journal of Algebra, 2003, 265(1):114-135.
[9] LYU J F, WANG X T, ZHUANG G B. DG Poisson algebra and its universal enveloping algebra[J]. Science China Mathematics, 2016, 59(5):849-860.
[10] CATTANEO A S, FIORENZA D, LONGONI R. Graded Poisson algebras[J]. Encyclopedia of Mathematical Physics, 2006(2):560-567.
[11] NASTASESCU C, TORRECILLAS B. Graded coalgebras[J]. Tsukuba Journal of Mathematics, 1993, 17(2):461-479.
[12] SWEEDLER M E.Hopf Algebras[M]. New York:Benjamin, 1969.
[13] UMBLE R N. The deformation complex for differential graded Hopf algebras[J]. Journal of Pure and Applied Algebra, 1996, 106(2):199-222.
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