KMS States on the Square of White Noise Algebra

. It was shown in [ AF S 00] that there are only three types of irreducible unitary representations θ of sl 2 . Using the Schurmann triple one can associate with each θ a number of representations of the square of white noise (SWN) algebra A . However, in analogy with the Boson, Fermion and q-deformed case, we expect that some interesting non irreducible representations of sl 2 may re-sult in GNS representations of KMS states associated with some evolutions on A . In the present paper determine the structure of the ∗ –endomorphisms of the SWN algebra, induced by linear maps in the 1–particle Hilbert algebra, we introduce the SWN analogue of the quasifree evolutions and find the explicit form of the KMS states associated with some of them.