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arXiv · 0705.3522

Small Bialgebras with a Projection: Applications

A. Ardizzoni·C. Menini
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Abstract

In this paper we continue the investigation started in [A.M.St.-Small], dealing with bialgebras $A$ with an $H$-bilinear coalgebra projection over an arbitrary subbialgebra $H$ with antipode. These bialgebras can be described as deformed bosonizations $R#_ξ H$ of a pre-bialgebra $R$ by $H$ with a cocycle $ξ$. Here we describe the behavior of $ξ$ in the case when $R$ is f.d. and thin i.e. it is connected with one dimensional space of primitive elements. This is used to analyze the arithmetic properties of $A$. Meaningful results are obtained when $H$ is cosemisimple. By means of Ore extension construction, we provide some examples of atypical situations (e.g. the multiplication of $R$ is not $H$-colinear or $ξ$ is non-trivial).

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A. Ardizzoni, C. Menini. 2007-05-24. Small Bialgebras with a Projection: Applications. https://doi.org/10.1080/00927870802623419

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