EXTENDING TABLE ALGEBRAS TO HOPF ALGEBRAS

Allen Herman, Gurmail Singh
2019 International Electronic Journal of Algebra  
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 an
more » ... an algebra-isomorphic group algebra. To illustrate our approach, we derive Hopf algebra comultiplications on table algebras of dimension 2 and 3. (2010) : 16T30, 05E30 Mathematics Subject Classification
doi:10.24330/ieja.586882 fatcat:ejeusr66svfl5kglef5olav5di