Lifting via cocycle deformation
Nicol\'as Andruskiewitsch, Iv\'an Angiono, Agust\'in Garc\'ia, Iglesias, Akira Masuoka, Cristian Vay
TL;DR
This paper introduces a method to compute all liftings of Nichols algebras over finite dimensional cosemisimple Hopf algebras using cocycle deformations, and analyzes their structural properties.
Contribution
It provides a systematic approach to classify liftings of Nichols algebras via cocycle deformations and investigates their structural characteristics.
Findings
All liftings can be obtained as cocycle deformations of bosonizations.
Characterization of the shape of liftings.
Framework applicable to finite dimensional cosemisimple Hopf algebras.
Abstract
We develop a strategy to compute all liftings of a Nichols algebra over a finite dimensional cosemisimple Hopf algebra. We produce them as cocycle deformations of the bosonization of these two. In parallel, we study the shape of any such lifting.
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