二重Poisson Hopf扩张
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摘要
通过类比法,给出了二重Poisson Hopf扩张的定义.利用Poisson Hopf代数的二重Poisson Ore扩张,并借助于系数对比法,得到了二重Poisson Hopf扩张的等价条件.所得结果推广了Poisson Hopf扩张的若干结论.
The definition of double Poisson Hopf extension was given by analogy. By studying the double Poisson Ore extension of Poisson Hopf algebras and using the coefficient contrast method, the equivalent condition for the double Poisson Hopf extension was obtained. The results extended some existed results about the Poisson Hopf extension.
The definition of double Poisson Hopf extension was given by analogy. By studying the double Poisson Ore extension of Poisson Hopf algebras and using the coefficient contrast method, the equivalent condition for the double Poisson Hopf extension was obtained. The results extended some existed results about the Poisson Hopf extension.
引文
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[8]Lü J F,OH S Q,WANG X T,et al.Enveloping algebras of double Poisson-Ore extension[J].Comm Algebra,2018,46(1):4891-4904.
[9]MONTGOMERY S.Hopf algebras and their actions on rings[M].Providence:CBMS Reg Conf Ser Math,1993.
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[11]BROWN K A,O’HAGAN S,ZHANG J J,et al.Connected Hopf algebras and iterated Ore extensions[J].J Pure Appl Algebra,2015,219(6):2405-2433.
[2]OH S Q.Poisson polynomial rings[J].Comm Algebra,2006,34(4):1265-1277.
[3]Lü J F,WANG X T,ZHUANG G B.Universal enveloping algebras of Poisson Hopf algebras[J].J Algebra,2015,426:92-136.
[4]Lü J F,WANG X T,ZHUANG G B.Universal enveloping algebras of Poisson Ore extension[J].Proc Amer Math Soc,2015,143(11):4633-4645.
[5]ZHANG J J,ZHANG J.Double Ore extensions[J].J Pure Appl Algebra,2008,212(12):2668-2690.
[6]ZHANG J J,ZHANG J.Double extension regular algebras of type (14641)[J].J Algebra,2007,322(2):373-409.
[7]CARVALHO P,LOPES S,MATCZUK J.Double Ore extensions versus iterated Ore extensions[J].Comm Algebra,2011,39(8):2838-2848.
[8]Lü J F,OH S Q,WANG X T,et al.Enveloping algebras of double Poisson-Ore extension[J].Comm Algebra,2018,46(1):4891-4904.
[9]MONTGOMERY S.Hopf algebras and their actions on rings[M].Providence:CBMS Reg Conf Ser Math,1993.
[10]KOROGODSKI L I,SOIBELMAN Y S.Algebras of functions on quantum groups,Part I[M].Providence:Amer Math Soc,1998.
[11]BROWN K A,O’HAGAN S,ZHANG J J,et al.Connected Hopf algebras and iterated Ore extensions[J].J Pure Appl Algebra,2015,219(6):2405-2433.