Deformed gauge transformations on deformed coordinate spaces are considered for any Lie algebra. The representation theory of this gauge group forces us to work in a deformed Lie algebra as well. This deformation rests on a twisted Hopf algebra, thus we can represent a twisted Hopf algebra on deformed spaces. That leads to the construction of Lagrangian invariant under a twisted Lie algebra.
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Wess, J. (2009). Differential Calculus and Gauge Transformations on a Deformed Space. In: Noncommutative Spacetimes. Lecture Notes in Physics, vol 774. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89793-4_1
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