# ALGEBRAIC COMBINATORICS

A construction of pairs of non-commutative rank 8 association schemes from non-symmetric rank 3 association schemes
Algebraic Combinatorics, Volume 4 (2021) no. 3, pp. 533-540.

We construct a pair of non-commutative rank $8$ association schemes from a rank $3$ non-symmetric association scheme. For the pair, two association schemes have the same character table but different Frobenius–Schur indicators. This situation is similar to that for the dihedral and quaternion groups of order $8$. We also determine the structures of adjacency algebras of the rank $8$ schemes over the rational number field.

Revised:
Accepted:
Published online:
DOI: https://doi.org/10.5802/alco.167
Classification: 05E30
Keywords: Character table, quaternion algebras, association schemes.
@article{ALCO_2021__4_3_533_0,
author = {Hanaki, Akihide and Yoshikawa, Masayoshi},
title = {A construction of pairs of non-commutative rank 8 association schemes from non-symmetric rank 3 association schemes},
journal = {Algebraic Combinatorics},
pages = {533--540},
publisher = {MathOA foundation},
volume = {4},
number = {3},
year = {2021},
doi = {10.5802/alco.167},
language = {en},
url = {https://alco.centre-mersenne.org/articles/10.5802/alco.167/}
}
Hanaki, Akihide; Yoshikawa, Masayoshi. A construction of pairs of non-commutative rank 8 association schemes from non-symmetric rank 3 association schemes. Algebraic Combinatorics, Volume 4 (2021) no. 3, pp. 533-540. doi : 10.5802/alco.167. https://alco.centre-mersenne.org/articles/10.5802/alco.167/

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