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For a finite group G and an algebraically closed field of characteristic zero we consider Artin-Schelter regular algebras A on which the Drinfeld double $D(G)$ acts inner faithfully, and its associated algebras of invariants AD(G). Explicit computations for the cases when G is the (generalized) quaternion group of order 8 and 16 are given.
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Kirkman et al. (2024) studied this question.
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