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math.RA2026
On the asymptotic Makar-Limanov rank conjecture
SiZhuo Yan, Hao Shen, Jianting Yang
Let be an algebraically closed field of characteristic zero and let be a nonconstant polynomial in finitely many freely noncommuting variables. We prove the asymptotic…
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 Volčič conjectured that a noncommutative polynomial belongs to the unital -algebra generated by finitely many noncommutative polynomials if and only if, for m…