Approximation of graded bialgebras

Giovanna Carnovale; Francesco Esposito; Lleonard Rubio y Degrassi

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arXiv · 2412.00234

Approximation of graded bialgebras

Giovanna Carnovale·Francesco Esposito·Lleonard Rubio y Degrassi

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Abstract

Motivated by an equivalence of categories established by Kapranov and Schechtman, we introduce, for each non-negative integer d, the category of connected bialgebras modulo d+1. We show that these categories fit into an inverse system of categories whose inverse limit category is equivalent to the category of connected bialgebras. In addition, we extend the notion of approximation of connected bialgebras to those that are not necessarily generated in degree 1 and show that, for connected bialgebras in the category of Yetter-Drinfeld modules over a Hopf algebra, approximation is compatible with cocycle twisting.

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BibTeX RIS

Giovanna Carnovale, Francesco Esposito, Lleonard Rubio y Degrassi. 2024-11-29. Approximation of graded bialgebras. https://arxiv.org/abs/2412.00234

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