On the Terwilliger algebra and quantum adjacency algebra of the Shrikhande graph
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 a...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | text |
| Published: |
Animo Repository
2020
|
| Subjects: | |
| Online Access: | https://animorepository.dlsu.edu.ph/faculty_research/11536 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | De La Salle University |
| Summary: | 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 . |
|---|