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Let A be a co-Poisson Hopf algebra with Poisson co-bracket δ. Here it is shown that the Hopf dual A˚ is a Poisson Hopf algebra with Poisson bracket {f,g}(x)=<δ(x),f[기호]g> for any f,g∈ A˚ 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.
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참고문헌 (4)
참고문헌 신청
A. Joseph / 1995 / Groups and Their Primitive Ideals, A series of modern surveys in mathematics, vol. 3 / Springer-Verlag : 29 ~
J. C. McConnell / 1987 / Noncommutative Noetherian Rings, Pure & Applied Mathematics, A Wiley-interscience series of texts, monographs & tracts / Wiley Inter-science
T. J. Hodges / 1997 / Algebraic structure of multi-parameter quantum groups / Advances in Math 126 : 52 ~ 92
V. Chari / 1994 / A Guide to Quantum Groups / Cambridge University Press
J. C. McConnell / 1987 / Noncommutative Noetherian Rings, Pure & Applied Mathematics, A Wiley-interscience series of texts, monographs & tracts / Wiley Inter-science
T. J. Hodges / 1997 / Algebraic structure of multi-parameter quantum groups / Advances in Math 126 : 52 ~ 92
V. Chari / 1994 / A Guide to Quantum Groups / Cambridge University Press
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