EXTENDING TABLE ALGEBRAS TO HOPF ALGEBRAS

Authors : Allen HERMAN, Gurmail SİNGH

Pages : 13-28

Doi:10.24330/ieja.586882

View : 15 | Download : 11

Publication Date : 2019-07-11

Article Type : Research Paper

Abstract :Let $A$ be a table algebra with standard basis $\mathbf{B}$, multiplication $\mu$, unit map $\eta$, skew-linear involution $*$, and degree map $\delta$.  In this article we study the possible coalgebra structures $insert ignore into journalissuearticles values(A,\Delta, \delta);$ on $A$ for which $insert ignore into journalissuearticles values(A, \mu, \eta, \Delta, \delta);$ 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 algebra-isomorphic group algebra.  To illustrate our approach, we derive Hopf algebra comultiplications on table algebras of dimension 2 and 3.
Keywords : Table algebra, Hopf algebra, fusion ring, association scheme