Table algebras

A Schur–Zassenhaus Theorem for association schemes

“…Subsets of S are called thin if they contain only thin elements. As a consequence, the scheme S itself is said to be thin if n s = 1 for each element s in S. 3 1 The first part of the theorem, which is relatively easy to prove, appears as Theorem 6.1; the second part needs the majority of the results obtained in this article and appears as Theorem 10.2. 2 We note that the definition of a scheme which we use in the present article differs from the more general definition given in [10].…”

“…In fact, the schemes which we consider in this article are exactly the schemes in the sense of [10] which are defined on finite sets. 3 Each thin scheme can be viewed in a natural way as a finite group; cf. [10,Theorem 5.5.1].…”

Fourier matrices of small rank

“…Since k 2 (2k 3 + 4) and k 3 (2k 2 + 4), we have (1,3), (1,6), (2,4), (2,8), (3,10), (4,6), (4,12), (6,16), (8,10), (12, 28)}.…”

“…Without loss of generality, we assume that the third irreducible character is a complex conjugate of the second character, thus k 2 = 1. Without loss of generality, let (1,4), (2,5), (3,6), (6,9)}.…”

Central Torsion Units of Integral Reality-Based Algebras With a Positive Degree Map

“…Reality-based algebras were introduced by Blau in [1] to provide a bridge between adjacency algebras of association schemes, table algebras, the C-algebras of Kawada, fusion rule algebras, and several other kinds of discrete hypergroups.…”