Nilpotency Property in Table Algebras

Table algebras form an important class of C-algebras. The dual of a table algebra may not be a table algebra, but just a C-algebra. It is not known under what conditions the dual of a table algebra is also a table algebra. In this paper we prove that if a table algebra has nilpotency property then its dual also is a table algebra. Finally we conclude that if (A, B) is a nilpotent table algebra then its dual also is a nilpotent table algebra.