Year: 2026
Type: preprint
Abstract: We characterize non-commutative polynomials of degree 2 which preserve free infinite divisibility as self-adjoint Lie polynomials of degree 2. This extends previous results which characterized homogeneous quadratic forms only. The proof is based on an involution of colored noncrossing partitions cancelling many terms; positive definiteness of the remaining terms is established by an explicit operator model on Fock space. Examples show that higher order Lie polynomials do not preserve free infinite divisibility.
Source: arXiv (Cornell University)
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Narodowym Centrum Nauki
OpenAlex ID: W7221834829