Even partition algebras P_n^2(δ) over ℂ are semisimple for all n if and only if δ is not a non-negative integer.
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Semisimplicity criterion for 2-tonal partition algebras
Even partition algebras P_n^2(δ) over ℂ are semisimple for all n if and only if δ is not a non-negative integer.