Toward the classification of normalized integral table algebras generated by a faithful non-real element of degree 3 with L1(B)={1} (I)

Abstract

The classification of integral table algebras (A, B) generated by a faithful element of degree 2 with $L_1(B)=\left\{1\right\}$ was completed by Blau in 1995. After that, it is an interesting topic to classify integral table algebras generated by a faithful non-real element of degree 3 with $L_1(B)=\left\{1\right\}.$ But it is difficult, so Arad and Chen et al. in 2005 and 2011 studied normalized integral table algebras generated by a faithful non-real element of degree 3 by assuming $L_1(B)=\left\{1\right\}$ and $L_2(B)=\varnothing ,$ they almost classified such table algebras. Here the authors continue this work but not assuming $L_2(B)=\varnothing .$

Communicated by Miriam Cohen

Keywords:

• Classification
• integral
• normalized
• table algebra

AMS CLASSIFICATION:

• 05E30
• 05E10
• 13A99

Acknowledgments

The authors would like to express their deep thanks to referee for his/her detailed, great, and constructive suggestions for revising this paper and refining the results, especially thanks to his/her selfless contribution of 36 detailed revising suggestions for the first version, 38 suggestions for the second version, and 21 suggestions for the third version of this paper, based on them we can overcome the gaps and errors, and make it better and more beautiful. Moreover the first author and the third author would like to express their thanks and deep respects to Prof. Zvi Arad (1942–2018) for his valuable suggestions and contributions in this research works.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11671324, 11971391).