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Deformation coproducts and differential maps

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Hudson R., Pulmannová S.

Studia Mathematica

2008

tom 188

nr 1

1-16

Let 𝒯 be the Itô Hopf algebra over an associative algebra 𝓛 into which the universal enveloping algebra 𝓤 of the commutator Lie algebra 𝓛 is embedded as the subalgebra of symmetric tensors. We show that there is a one-to-one correspondence between deformations Δ[h] of the coproduct in 𝒯 and pairs (d⃗[h],d⃖[h]) of right and left differential maps which are deformations of the differential maps for 𝒯 [Hudson and Pulmannová, J. Math. Phys. 45 (2004)]. Corresponding to the multiplicativity and coassociativity of Δ[h], d⃗[h] and d⃖[h] satisfy the Leibniz-Itô formula and a mutual commutativity condition. Δ[h] is recovered from d⃗[h] and d⃖[h] by a generalised Taylor expansion. As an illustrative example we consider the differential maps corresponding to the quantisation of quasitriangular commutator Lie bialgebras of [Hudson and Pulmannová, Lett. Math. Phys. 72 (2005)].

Ograniczanie wyników

1 Studia Mathematica

1 Hudson R.

1 Pulmannová S.

1 2008

Wyniki wyszukiwania

Deformation coproducts and differential maps