Planar algebras associated to Latin squares are of subgroup-group-type
Authors:
Vijay Kodiyalam and Sruthy Murali
Journal:
Proc. Amer. Math. Soc. 149 (2021), 163-172
MSC (2010):
Primary 46L37
DOI:
https://doi.org/10.1090/proc/15073
Published electronically:
October 16, 2020
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: Latin squares naturally yield planar subalgebras of the spin planar algebra. We show that all of these are of subgroup-group-type.
- [1] Ved Prakash Gupta, Planar algebra of the subgroup-subfactor, Proc. Indian Acad. Sci. Math. Sci. 118 (2008), no. 4, 583–612. MR 2511128, https://doi.org/10.1007/s12044-008-0046-0
- [2] Vaughan F. R. Jones, Planar algebras, math/9909027, 1999.
- [3] Vaughan F. R. Jones, Scott Morrison, and Noah Snyder, The classification of subfactors of index at most 5, Bull. Amer. Math. Soc. (N.S.) 51 (2014), no. 2, 277–327. MR 3166042, https://doi.org/10.1090/S0273-0979-2013-01442-3
- [4] Vijay Kodiyalam, Sruthymurali, Sohan Lal Saini, and V. S. Sunder, On a presentation of the spin planar algebra, Proc. Indian Acad. Sci. Math. Sci. 129 (2019), no. 2, Paper No. 27, 11. MR 3922286, https://doi.org/10.1007/s12044-019-0472-1
- [5] Vijay Kodiyalam, Sruthy Murali, and V. S. Sunder, Planar algebras, quantum information theory and subfactors, arXiv1912.07228 [math.OA], 2019.
- [6] Brendan McKay, Combinatorial data page, https://users.cecs.anu.edu.au/~bdm/data/latin.html.
- [7] Benjamin Musto and Jamie Vicary, Quantum Latin squares and unitary error bases, Quantum Inf. Comput. 16 (2016), no. 15-16, 1318–1332. MR 3616029
- [8] David J. Reutter and Jamie Vicary, Biunitary constructions in quantum information, High. Struct. 3 (2019), no. 1, 109–154. MR 3939047
Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 46L37
Retrieve articles in all journals with MSC (2010): 46L37
Additional Information
Vijay Kodiyalam
Affiliation:
The Institute of Mathematical Sciences, Chennai, India
Email:
vijay@imsc.res.in
Sruthy Murali
Affiliation:
The Institute of Mathematical Sciences, Chennai, India
Email:
sruthym@imsc.res.in
DOI:
https://doi.org/10.1090/proc/15073
Received by editor(s):
December 19, 2019
Received by editor(s) in revised form:
January 31, 2020
Published electronically:
October 16, 2020
Communicated by:
Adrian Ioana
Article copyright:
© Copyright 2020
American Mathematical Society