Generalized table algebras

Arad, Zvi; Fisman, Elsa; Muzychuk, Mikhail

doi:10.1007/bf02785571

Cited by 117 publications

(135 citation statements)

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“…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)}.…”

Section: Fourier Matrices Of Rankmentioning

confidence: 99%

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Fourier matrices of small rank

Singh¹

2017

Journal of Algebra Combinatorics Discrete Structures and Applications

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Modular data is an important topic of study in rational conformal field theory. Cuntz, using a computer, classified the Fourier matrices associated to modular data with rational entries up to rank 12, see [3]. Here we use the properties of C-algebras arising from Fourier matrices to classify complex Fourier matrices under certain conditions up to rank 5. Also, we establish some results that are helpful in recognizing C-algebras that not arising from Fourier matrices by just looking at the first row of their character tables.2010 MSC: 05E30, 05E99, 81R05

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Section: Fourier Matrices Of Rankmentioning

confidence: 99%

“…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)}.…”

Section: Fourier Matrices Of Rankmentioning

confidence: 99%

Fourier matrices of small rank

Singh¹

2017

Journal of Algebra Combinatorics Discrete Structures and Applications

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“…We have the following equations on intersection numbers (see [1], [2], [13] or [14]): Lemma 2.1. We have the following:…”

Section: Preliminariesmentioning

confidence: 99%

COMMUTATIVITY OF ASSOCIATION SCHEMES OF ORDER pq

Hanaki¹,

Hirasaka²

2013

East Asian mathematical journal

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Abstract. Let (X, S) be an association scheme where X is a finite set and S is a partition of X × X. The size of X is called the order of (X, S). We define C to be the set of positive integers m such that each association scheme of order m is commutative. It is known that each prime is belonged to C and it is conjectured that each prime square is belonged to C. In this article we give a sufficient condition for a scheme of order pq to be commutative where p and q are primes, and obtain a partial answer for the conjecture in case where p = q.

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“…In the rest of this article, we will only use these matrices and show that (A, B) is an ISGT-algebra [1]. For any x ∈ B, we can write…”

Section: Constructionmentioning

confidence: 99%

“…If such an association scheme has a non-normal closed subset with two relations, then it defines a 2-design. Conversely, it was shown that some parameters of 2-designs define ISGT-algebras (integral standard generalized table algebras in the sense of [1]). But it was not determined which kind of parameters define ISGT-algebras.…”

Section: Introductionmentioning

confidence: 99%