Multiplicativity of the JLO-character

We prove that the Jaffe-Lesniewski-Osterwalder character is compatible with the $A_{\infty}$-structure of Getzler and Jones.

💡 Research Summary

The paper establishes that the Jaffe‑Lesniewski‑Osterwalder (JLO) character, a cyclic cocycle associated with a spectral triple ((\mathcal{A},\mathcal{H},D)), is multiplicative with respect to the tensor product of spectral triples and that this multiplicativity is fully compatible with the (A_{\infty})‑algebra structure introduced by Getzler and Jones.

The authors begin by recalling the classical definition of the JLO character: for a self‑adjoint unbounded operator (D) on a Hilbert space (\mathcal{H}) and a dense *‑subalgebra (\mathcal{A}\subset B(\mathcal{H})), the (n)-cochain is given by an integral over the standard simplex (\Delta^{n}) of a trace involving the heat semigroup (e^{-tD^{2}}) and commutators (