| For a tuple A = (A1, A2, ..., An) of elements in a unital topological algebra B , the projective spectrum, P(A) is the set of z ∈ Cn such that the linear pencil A(z) = z1A1 + z2A2 + · · · + znAn is not invertible in B . The Maurer-Cartan type B -valued one-form oA := ( A(z))--1dA( z) appears to contain much information about the tuple A. Here, oA will establish a Jacobi type formula in the finite dimensional case. Furthermore, o A giver rise to a map between the cyclic cohomology, HC*( BA ) and the de Rham cohomology of the projective resolvent H*d (Pc(A)). |
