Terwilliger Algebras of Group Association Schemes of Matrix Groups

Nur Hamid

Abstract


This paper investigates the Terwilliger algebras of some group association schemes related to matrix groups. We obtain the structure of the Terwilliger algebras for the general and the special linear group of 2 × 2 matrices over the field of order 5. In particular, we determine the Wedderburn decomposition of these algebras.


Keywords


Terwilliger algebra; Association Scheme; Matrix Group

Full Text:

PDF

References


J. M. P. Balmaceda and M. Oura, The Terwilliger algebras of the group association schemes of S5 and A5, Kyushu J. Math. 48 (1994), no. 2, 221-231.

J. M. P. Balmaceda and A. C. L. Reyes, Terwilliger algebras of certain group association schemes, Journal of the Math. Soc. Philippines. 44 (2021), no. 2, 19-28.

E. Bannai and A. Munemasa, The Terwilliger algebras of group association schemes, Kyushu J. Math. 49 (1995), no. 1, 93-102.

N. L. Bastian, Terwilliger algebras for several finite groups, Thesis and Dissertation, (2021), https://scholarsarchive.byu.edu/etd/8997 posted 22 March 2021.

N. Hamid and M. Oura, Terwilliger Algebras of Some Group Association Schemes, Math. J. Okayama Univ. 61 (2019), 199-204.

A. Hanaki, Modular Terwilliger Algebras of Association Schemes, Graphs and Combinatorics 37 (2021), 1521–1529, https://doi.org/10.1007/s00373-021-02363-0

R. Maleki, On the Terwilliger algebra of the group association scheme of Cn ⋊ C2 Discrete Mathematics (2024), 113773, https://doi.org/10.1016/j.disc.2023.113773.

SageMath, the Sage Mathematics Software System (Version 9.0), The Sage Developers, 2020, https://www.sagemath.org.

P. Terwilliger, The subconstituent algebra of an association scheme I, J. Algebraic Combin. 1 (1992), no. 4, 363–388, II. 2 (1993), no. 1, 73–103, III. 2 (1993), no. 2, 177–210.

J. Yang, X. Zhang, L. Feng, The Terwilliger algebras of the group association schemes of three metacyclic groups, J. Comb. Des. 32, 8 (2024), https://doi.org/10.1002/jcd.21941. 1063-8539




DOI: http://dx.doi.org/10.12962/j24775401.v11i1.21470

Refbacks

  • There are currently no refbacks.



View My Stats


Creative Commons License
International Journal of Computing Science and Applied Mathematics by Pusat Publikasi Ilmiah LPPM, Institut Teknologi Sepuluh Nopember is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Based on a work at https://iptek.its.ac.id/index.php/ijcsam.