3 papers
math.RA2026
Noncommutative Rational Sums of Squares in Free Algebras
Sizhuo Yan, Jianting Yang, Lihong Zhi
This paper introduces rational sums of squares for symmetric noncommutative polynomials in free algebras. Under the assumption that the polynomial admits a strictly positive scalar…
math.RA2026
A Homogeneous Nullstellensatz for Joint Invariant Subspaces
Sizhuo Yan, Jianting Yang, Lihong Zhi
Jurij VolÄiÄ conjectured that a noncommutative polynomial belongs to the unital -algebra generated by finitely many noncommutative polynomials if and only if, for…
math.OC2025
Sparse sum of Hermitian squares in group algebras of finite groups
Jianting Yang, Ke Ye, Lihong Zhi
Nonnegative elements in group algebras play a central role in harmonic analysis, operator algebras, and computational optimization. This paper investigates sparse sum-of-Hermitian-…