Small Bialgebras with a Projection: Applications

Details Small Bialgebras with a Projection: Applications Small Bialgebras with a Projection: Applications

2007-05-24

arxiv.org/abs/0705.3522v1

Mathematics

Quantum Algebra

Scientific paper

10.1080/00927870802623419

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 $R#_{\xi} H$ of a pre-bialgebra $R$ by $H$ with a cocycle $\xi$. Here we describe the behavior of $\xi$ 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 $\xi$ is non-trivial).

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