We construct a pair of non-commutative rank association schemes from a rank 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 . We also determine the structures of adjacency algebras of the rank schemes over the rational number field.
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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 = {http://www.numdam.org/articles/10.5802/alco.167/} }
TY - JOUR AU - Hanaki, Akihide AU - Yoshikawa, Masayoshi TI - A construction of pairs of non-commutative rank 8 association schemes from non-symmetric rank 3 association schemes JO - Algebraic Combinatorics PY - 2021 SP - 533 EP - 540 VL - 4 IS - 3 PB - MathOA foundation UR - http://www.numdam.org/articles/10.5802/alco.167/ DO - 10.5802/alco.167 LA - en ID - ALCO_2021__4_3_533_0 ER -
%0 Journal Article %A Hanaki, Akihide %A Yoshikawa, Masayoshi %T A construction of pairs of non-commutative rank 8 association schemes from non-symmetric rank 3 association schemes %J Algebraic Combinatorics %D 2021 %P 533-540 %V 4 %N 3 %I MathOA foundation %U http://www.numdam.org/articles/10.5802/alco.167/ %R 10.5802/alco.167 %G en %F ALCO_2021__4_3_533_0
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. http://www.numdam.org/articles/10.5802/alco.167/
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