We study the projective linear group PGL2(A) associated with an arbitrary algebra A, and its subgroups from the point of view of their action on the space of involutions in A. This action formally resembles Möbius transformations known from complex geometry. By specifying A to be an algebra of bounded operators in a Hilbert space H, we rediscover the Möbius group μev(M) defined by Connes and st...

Let L be a self-adjoint invertible operator in Hilbert space such that − 1 is p -summable. Under certain discrete dimension spectrum assumption on , we study the relation between (regularized) Fredholm determinant, det ( I + z ⋅ ) one hand and zeta regularized ζ other. One of main results formula = exp ⁡ ∑ j ! d log | 0 . We show derivatives can expressed terms values heat trace coefficients Fu...

We study the projective linear group PGL 2 (A) associated with an arbitrary algebra A and its subgroups from the point of view of their action on the space of involutions in A. This action formally resembles M obius transformations known from complex geometry. By specifying A to be an algebra of bounded operators in a Hilbert space H, we rediscover the Mobius group ev (M) de ned by Connes and...