Some properties of the symmetric enveloping algebra of a subfactor, with applications to amenability and property \(T\)
In order to gain more insight into the structure of subfactors \(N\subset M\) with finite Jones index, the author in [Math. Res. Lett. 1, No. 4, 409-425 (1994; Zbl 0902.46042)] introduced its symmetric enveloping algebra and the corresponding symmetric enveloping inclusion. In the present paper he undertakes a more detailed study of these objects, in particular, explores the question of amenability and property \(T\). For \(II_1\) factors it turns out that the symmetric enveloping algebra is amenable (i.e. hyperfinite) if and only if \(N\), \(M\), and the standard graph \(\Gamma_{N,M}\) are amenable. Moreover, as the main result he proves that amenability of subfactors is inherited by inclusions, thereby generalizing \textit{A. Connes}' hereditarity result for hyperfinite \(II_1\) factors [Ann. of Math., II. Ser. 104, 73-115 (1976; Zbl 0343.46042)].
scientific article; zbMATH DE number 1388238