JOURNAL BROWSE
Search
Advanced SearchSearch Tips
DUALITY OF CO-POISSON HOPF ALGEBRAS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
DUALITY OF CO-POISSON HOPF ALGEBRAS
Oh, Sei-Qwon; Park, Hyung-Min;
  PDF(new window)
 Abstract
Let A be a co-Poisson Hopf algebra with Poisson co-bracket . Here it is shown that the Hopf dual is a Poisson Hopf algebra with Poisson bracket {f, g}(x) = < , > for any f, g and x A if A is an almost normalizing extension over the ground field. Moreover we get, as a corollary, the fact that the Hopf dual of the universal enveloping algebra U(g) for a finite dimensional Lie bialgebra g is a Poisson Hopf algebra.
 Keywords
co-Poisson Hopf algebra;Poisson Hopf algebra;
 Language
English
 Cited by
1.
Co-poisson structures on polynomial Hopf algebras, Science China Mathematics, 2017, 1869-1862  crossref(new windwow)
 References
1.
V. Chari and A. Pressley, A Guide to Quantum Groups, Cambridge University Press, Providence, 1994.

2.
T. J. Hodges, T. Levasseur, and M. Toro, Algebraic structure of multi-parameter quantum groups, Advances in Math. 126 (1997), 52-92. crossref(new window)

3.
A. Joseph, Quantum Groups and Their Primitive Ideals, A series of modern surveys in mathematics, vol. 3. Folge.Band 29, Springer-Verlag, 1995.

4.
J. C. McConnell and J. C. Robson, Noncommutative Noetherian Rings, Pure & Applied Mathematics, A Wiley-interscience series of texts, monographs & tracts, Wiley Inter-science, New York, 1987.