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Let A be a table algebra with standard basis B, multiplication µ, unit map η, skew-linear involution * , and degree map δ. In this article we study the possible coalgebra structures (A, ∆, δ) on A for which (A, µ, η, ∆, δ) becomes a Hopf algebra with respect to some antipode. We show that such Hopf algebra structures are not always available for noncommutative table algebras. On the other hand, commutative table algebras will always have a Hopf algebra structure induced from andoi:10.24330/ieja.586882 fatcat:ejeusr66svfl5kglef5olav5di