On the Terwilliger algebra and quantum adjacency algebra of the Shrikhande graph
College
College of Science
Department/Unit
Mathematics and Statistics Department
Document Type
Article
Source Title
Manila Journal of Science
Volume
13
First Page
31
Last Page
39
Publication Date
2020
Abstract
Let XX denote the vertex set of the Shrikhande graph. Fix xx x . Associated with xx is the Terwilliger algebra TT T TT T T of the Shrikhande graph, a semisimple subalgebra of MatXX(C). There exists a subalgebra QQ QQ of TT that is generated by the lower- ing, flat, and raising matrices in TT . The algebra QQ is semisimple and is called the quan- tum adjacency algebra of the Shrikhande graph. Terwilliger & Zitnik (2019) investigated how QQ and TT are related for arbitrary distanceregular graphs using the notion of quasi- isomorphism between irreducible TT modules. Using their results, together with descrip- tion of the irreducible TT modules of the Shrikhande graph by Tanabe (1997), we show in this paper that for the Shrikhande graph, we have QQ Q .
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Recommended Citation
Morales, J. S., & Palma, T. M. (2020). On the Terwilliger algebra and quantum adjacency algebra of the Shrikhande graph. Manila Journal of Science, 13, 31-39. Retrieved from https://animorepository.dlsu.edu.ph/faculty_research/11536
Disciplines
Algebra | Algebraic Geometry
Keywords
Graph connectivity; Graph theory
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