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Implement the face semigroup of a hyperplane arrangement and provide a custom class for the algebra #38709

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tscrim opened this issue Sep 25, 2024 · 0 comments

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tscrim commented Sep 25, 2024

The face semigroup algebra of a hyperplane arrangement is implemented as an instance of the FiniteDimensionalAlgebra. We should first provide a direct implementation of the face semigroup as a stand-alone parent. Then using that, we should implement a custom class for the algebra (possibly a subclass of FiniteDimensionalAlgebra, but the most likely candidate would be as a subclass of CombinatorialFreeModule whose basis is the semigroup). This will give it more features and a direct link to the hyperplane arrangement.

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