Bialgebra Structures On Table Algebras

A bialgebra is both a unital associative algebra and a coassociative coalgebra A over a field K whose algebra and coalgebra structures satisfy certain compatibility conditions. A table algebra A is an algebra over with distinguish basis and involution that satisfies certain conditions. In this paper, we establish a process to find bialgebra structures on commutative table algebras and using that we find bialgebra structures on table algebras of dimensions 2 and 3.