Duality of co-Poisson Hopf algebras
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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.
Abstract
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.
참고문헌 (4)
- V. Chari, "A Guide to Quantum Groups" (1994), Cambridge University Press
- T. J. Hodges, "Algebraic structure of multi-parameter quantum groups", Advances in Math, 126, pp.52~92 (1997)
- A. Joseph, "Groups and Their Primitive Ideals, A series of modern surveys in mathematics, vol. 3", pp.29~ (1995), Springer-Verlag
- J. C. McConnell, "Noncommutative Noetherian Rings, Pure & Applied Mathematics, A Wiley-interscience series of texts, monographs & tracts" (1987), Wiley Inter-science