| Résume | Bozejko and Speicher constructed tracial von Neumann algebras, the construction being a generalized version of Voiculescu's free Gaussian functor. Hiai later generalized this construction to q-deformed Araki–Woods algebras associated with orthogonal representations of real numbers. Further, these algebras were generalized by Bikram-Kumar-Mukherjee replacing q by an appropriate real matrix and a decomposition of the associated Hilbert space into invariant subspaces of the action (called these algebra mixed q-deformed Araki-Woods algebras). Several properties have been investigated concerning this von Neumann algebra amongst which factoriality turns out to the most trickiest one. Simplicity of C*-algebras is analogous to the factoriality of von Neumann algebras. In this talk, we discuss recent progress on the simplicity of these algebras when viewed as C*-algebras. First, we briefly describe the construction of mixed q-deformed Araki-Woods C*-algebras. Then we will talk about the simplicity of these C*-algebras. In particular we show that the mixed q-deformed Araki-Woods C*-algebras are simple when the underlying Hilbert space in the construction is infinite-dimensional and the analytic generator of the associated orthogonal representation is bounded. This is a joint work with Prof. Kunal Krishna Mukherjee (IIT Madras) and Prof. Issan Patri (ISI Delhi) |
