Deformation coproducts and differential maps

• Autorzy: R. L. Hudson , S. Pulmannová
• Języki publikacji: EN

Abstrakty

EN

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)].

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2008
• Tom: 188
• Numer: 1
• Strony: 1-16

Daty

wydano

2008

Twórcy

autor

R. L. Hudson

• Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire, LE11 3TU, Great Britain

autor

S. Pulmannová

• Mathematical Institute, Slovak Academy of Sciences, Stefankova 49, 81473 Bratislava, Slovakia

Identyfikatory

DOI

10.4064/sm188-1-1