New PDF release: Diàlogos del orador

By Cicero Marcus Tullius

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Sample text

Asaeda, U. Haagerup  u f C 2,l u =     f E 3,l f 4 =u β 2 +1 β 2 −2  = −1 β 2 −2 0 0 0 0 0 0 0 0 0 4 −(β √ 2 −2) 4 +4) 2(β  2β  −1 √  2 β 4 +4  2 √1 √β −2 β 2 +1 2(β 4 +4) u  e 4 2,r ∗  ∗   ∗ −1 u  −1  = 0 −1 u e 4 2,r −1 β 2 +1 −1 3,l β √ 2 2 0 √ − 2β −1 2 β√+1 β 2 +1 − 2β −β 2 2 −1) β 2 +1 2(β√ β2 − 2β β 2 +1 β 2 +1 f f E  0   0   β2  , 2 β√+1   − 2β  2 β +1  √ 1 β 2 −2 √  β 2 +1  2  β −2 0 e 4 2,r ,  0 0  −4β 2 −(β 4 −4)  . β 4 +4 β 4 +4  −(β 4 −4) 4β 2 β 4 +4 β 4 +4 Here note u(g-4) = −1.

In this case there is no direct analytic connection (such as Morita equiva∗ ( ). g. [21]). Moreover, since H 2 ( ; T) T, there exists a one-parameter family of twisted group C*-algebras which can be regarded ∗ ( ). as deformations of Cred The group will be regarded as a discrete cocompact subgroup of PSU(1,1). The latter acts on the unit disc D by linear fractional transformations and hence induces the holomorphic covering map D/ → . The C*-algebra C( ) is identified with the algebra of continuous -invariant functions on D.

Haagerup c˜g  d˜ c˜e ˜ 0 C˜ d   ˜ Ed  0    2 √ 2 (β +1) β −1 √ Ef   2β 3  =  5 Ed  0    β 4 −1 Gf   − 2β 6  β 2 −2 Gh 2β 2 −1 β 2 −2 β2 √ −(β 2 −2) (β 2 +1)(2β 2 −1) 1 2β 2 β 2 −2 β 2 +1 β 2 −1 β 2 −2 1 β2 0 e3e e2e β 2 (β 2 −2) −1 2β 2 −1 − β 4 +4 β 2 −2 2β 2 −1 β2 (β 4 +4)(β 2 +1) β 2 +3 (β 2 +3)(2β 2 −1) β2 β 2 (β 2 −1) β 4 +4 Ab f = 2 d   C    b C d 0 β 2 +1 2β 2 −1 0 0 1 β2 0 0 β 2 +1 2β 2 −1 ec ga β 2 −1 2β 2 (β 2 −2) √ β 2 +1 gc −√ − β 21−1 √ 1 2(β 2 −1) β 4 −1 2β 2 (β 2 −2) 0 β 2 (β 2 −2) − 2β1 2 β 2 −1 2β 2 β 2 +1 β2 0 β 2 (β 4 +4) β 2 +1 2(β 2 −1) − 0 β 2 +3 0 √ √ 4 2(β 4 +4) √ 2 √2 β −1 0  β −2 β2 √ β 2 −1 √ β 2 (β 2 +2) (β 2 +1)(β 4 +4) − eg 4(β 2 −2) (β 2 +3)(2β 2 −1) √ − β 2 −1 √ 2 ec˜ 2 4(β 2 +1)           ,             ,   = d˜ 3  e2e e3e ec β 4 +4 E  0 β 2 (β 2 +1)   β 4 −4 −1 2 Ef  β 2 (β 2 −1)(β 4 +4) β 2 −1 β 2 (β 4 +4)  √  2 2 β −2 2(β −2) Ed   − (2β 2 −1)(β 2 −1)√2(β 4 +4) − (2β 2 −1)√β 4 +4   2 2 2 −2) Cd − √ β 2(β −2) − √ 4(β 3 4 4 2 (2β −1) (β +4) (β +4)(2β −1) 0 0 √ 4 β 2 (β 2 −1) − 2β 21−1 ce 1 β2 β 2 −2 β 2 +1       , β2  √ (2β 2 −1)3 (β 2 +1)    6 2 β 2 −2 β 2 −1 β (β −2) (2β 2 −1)3 Exotic Subfactors of Finite Depth with Jones Indices d˜ 49 = d˜ 3  e2e e3e β 2 (β 2 −2) (β 2 +1)(2β 2 −1)(β 4 +4) −2) 2(β 4 +4) 2(β −√ E  −   3 2 f  E  − 2β2β2 −1 √ 2 β 4 (β +1)(β +4)   2 (β 2 +2) d  E  2β 21−1 (ββ2 +1)(β 4 +4)   2 (β 2 +2) C d 2 2β 22−1 (ββ2 +1)(β 4 +4) 2β 2 2 2β 2 −1 2 √  d = 4 2(β 4 +4) gc  , √ √−2 2 2β 2 −1 0 β3 (β 2 +1)(β 4 +4) (2β 2 −1)(β 4 −4) 1 2(β 4 +4) β 2 (β 2 −1) − 2β 4 (β 2 +1)(β 4 +4) − 21 −1 √ (2β 2 −1) β 2 +1 4β 2 (β 2 +1)(β 4 +4) √ 0 2β 2 −1 2β 2 (β 2 −3) − 2β 21−1 √ ec − β14 √ β 2 +1 β 2 −2 β 2 (2β 2 −1) (β 2 −1)(β 4 +4) 0 2(β 2 +1) β 4 +4 4β 2 (β 2 +1)(β 4 +4) β(β −2) 2β 2 −1 e2e √ √−2 2 (β 2 −1)3 0 1 2β 2 −1 ge √ 2 √ 2 2β 2 −1 1 2β 2 −1 ge e3e √ √2 2 2β 2 −1 − 2β 21−1 0 √ 2 β 2 −1 β3         ,            β 2 +1  ,  2 β −2 1  β 2 +1 2β 2 −1    2 5−β 2 gc ge 1 0 , 0 1 C − 2β 21−1  √ E d √2 22 2β −1 g  √c − β 2 +1 C d  β4   −1 Cb   β 2 −2  ˜ = Ed  0  3  f  E  0  √  2 β 4 −1 d E β3 0 β 2 −2 β 2 +1 2 2β 2 −1 2 4 2(β 4 +4) Cb Ef = 3 √ c˜e 0 (β 2 +1)(β 4 +4) 1 2β 2 −1 3 f 4β 2 2β 2 −1 h h˜ 2 ec β3 (β 2 +1)(β 4 +4) 50 M.

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Diàlogos del orador by Cicero Marcus Tullius


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