A finiteness result for commuting squares of matrix algebras

Journal of Operator Theory

Volumn 55, Issue 2, 2006, Pages 295-310

  Nicoarǎ, Remus ^a,b  

^a VANDERBILT UNIVERSITY   (United States)

^b INSTITUTE OF MATHEMATICS   (Romania)

Author keywords

Commuting squares; Complex Hadamard matrices; Subfactors

Indexed keywords

EID: 33749642023     PISSN: 03794024     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (12)

1. n, whose Fourier transforms have constant modulus, and "cyclic n-roots", in Recent Advances in Fourier Analysis and its Applications, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., vol. 315, Kluwer Acad. Publ., Dordrecht, 1990, pp. 131-140.
2. E. CHRISTENSEN, Subalgebras of a finite algebra, Math. Ann. 243(1979), 17-29.
3. U. HAAGERUP, Orthogonal maximal abelian *-subalgebras of the n x n matrices and cyclic n-roots, in Operator Algebras and Quantum Field Theory (ed. S. Doplicher et al.), International Press, town 1997, pp. 296-322.
4. P. DE LA HARPE, V.F.R. JONES, Paires de sous-algebres semi-simples et graphes fortement reguliers, C.A. Acad. Sci. Paris Ser. I Math. 311(1990), 147-150.
5. V.F.R. JONES, Index for subfactors, Invent. Math. 72(1983), 1-25.
6. V.F.R. JONES, V.S. SUNDER, Introduction to subfactors, London Math. Soc. Lecture Notes Ser., vol. 234, Cambridge Univ. Press, Cambridge 1997.
7. A. MUNEMASA, Y. WATATANI, Orthogonal pairs of *-subalgebras and association schemes, C.R. Acad. Sci. Paris Ser. I Math. 314(1992), 329-331.
8. M. PETRESCU, Existence of continuous families of complex Hadamard matrices of certain prime dimensions and related results, Ph.D. Dissertation, University of California Los Angeles, Los Angeles 1997.
9. S. POPA, Classification of subfactors: the reduction to commuting squares, Invent. Math. 101(1990), 19-43.
10. S. POPA, Classification of amenable subfactors of type II, Acta Math. 172(1994), 163-255.
11. S. POPA, Othogonal pairs of *-subalgebras in finite von Neumann algebras, J. Operator Theory 9(1983), 253-268.
12. W. SZYMANSKI, Finite index subfactors and Hopf algebra crossed products, Proc. Amer. Math. Soc. 120(1994), 519-528.