Application of an algorithm computes Gröbner-Shirshov bases in double extension algebras, suggesting a PBW basis exists.
In this paper, we compute the Gröbner-Shirshov bases for certain regular double extension algebras by means of an algorithm implemented in Matlab, which facilitates the underlying algebraic computations. Moreover, we establish that these families also admit a PBW basis.
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Herrera et al. (2025) studied this question.
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