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math.QA2022
The Exponential Map for Hopf Algebras
Ghaliah Alhamzi, Edwin Beggs
We give an analogue of the classical exponential map on Lie groups for Hopf -algebras with differential calculus. The major difference with the classical case is the interpretat…
math.QA2020
Matrices, Bratteli Diagrams and Hopf-Galois Extensions
Ghaliah Alhamzi, Edwin Beggs
We show that the matrix embeddings in Bratteli diagrams are iterated direct sums of Hopf-Galois extensions (quantum principle bundles) for certain abelian groups. The corresponding…
math.QA2013★ 10 cited
From homotopy to Ito calculus and Hodge theory
Ghaliah Alhamzi, Edwin Beggs, Andrew Neate
We begin with a deformation of a differential graded algebra by adding time and using a homotopy. It is shown that the standard formulae of Itô calculus are an example, with four c…