Double product integrals and Enriquez quantization of Lie bialgebras I: The quasitriangular identities
| Autor: | R. L. Hudson, S. Pulmannová |
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| Rok vydání: | 2004 |
| Předmět: | |
| Zdroj: | Journal of Mathematical Physics. 45:2090-2105 |
| ISSN: | 1089-7658 0022-2488 |
| Popis: | Let T(L) be the space of all tensors over a Lie algebra L in which the Lie bracket is obtained by taking commutators in an associative algebra. We show that T(L) becomes a Hopf algebra when equipped with a noncommutative modification of the shuffle product together with the standard coproduct. A definition is given of directed double product integrals as iterated single product integrals driven by formal power series with coefficients in the tensor product of L with an appropriate associative algebra. For the Hopf algebra T(L)[[h]] of formal power series we show that elements R[h] of (T(L)⊗T(L))[[h]] satisfying (Δ⊗id)R[h]=R[h]13R[h]23, (id⊗Δ)R[h]=R[h]13R[h]12,and which are unitalized by the counit in either copy of T(L), can be characterized as such directed double product integrals ∏∏(1+d⊗d↙r[h]) where r[h] is a formal power series with coefficients in L⊗L and vanishing constant term. |
| Databáze: | OpenAIRE |
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