We prove that the arithmetic Hecke operators are completely positive maps with respect to the Berezin's quantization deformation product of functions on H/Gamma. We then show that the associated subfactor defined by the Connes's correspondence associated to the completely positive map has integer index and graph A(infinity). The same construction for PSL(3, Z) gives a finite index subfactor of L(PSL(3, Z)) of infinite depth.
Radulescu, F. (1996). Arithmetic Hecke operators as completely positive maps. COMPTES RENDUS DE L'ACADÉMIE DES SCIENCES. SÉRIE 1, MATHÉMATIQUE, 322(6), 541-546.
Arithmetic Hecke operators as completely positive maps
RADULESCU, FLORIN
1996-01-01
Abstract
We prove that the arithmetic Hecke operators are completely positive maps with respect to the Berezin's quantization deformation product of functions on H/Gamma. We then show that the associated subfactor defined by the Connes's correspondence associated to the completely positive map has integer index and graph A(infinity). The same construction for PSL(3, Z) gives a finite index subfactor of L(PSL(3, Z)) of infinite depth.File in questo prodotto:
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