No abstract

For a tuple A = (A 1 , A 2 , ..., A n ) of elements in a unital algebra B over C, its projective spectrum P (A) or p(A) is the collection of z ∈ C n , or respectively z ∈ P n−1 such that the multi-parameter pencilIn commutative cases, invariant multi-linear functionals are effective tools to extract that information. This paper shows that in noncommutative cases, the cyclic cohomology of B does a similar job. In fact, a Chen-Weil type map κ from the cyclic cohomology of B to the de Rham cohomology H * d (P c (A), C) is established. As an example, we prove a closed high-order form of the classical Jacobi's formula.1991 Mathematics Subject Classification. Primary 47A13; Secondary 55N20. Key words and phrases. cyclic cohomology, invariant multilinear functional, Maurer-Cartan form, maximal ideal space, projective spectrum, projective resolvent set, de Rham cohomology, union of hyperplanes.