6 papers
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…
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…
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…
The non-Archimedean Nirgendsnegativsemidefinitheitsstellensatz is not true
Hao Liang, Sizhuo Yan, Jianting Yang +1
Klep and Schweighofer asked whether the Nirgendsnegativsemide-finitheitsstellensatz holds for a symmetric noncommutative polynomial whose evaluations at bounded self-adjoint operat…
A Characterization of Perfect Strategies for Mirror Games
Sizhuo Yan, Jianting Yang, Tianshi Yu +1
We associate mirror games with the universal game algebra and use the *-representation to describe quantum commuting operator strategies. We provide an algebraic characterization o…
Extensions of S-Lemma for Noncommutative Polynomials
Feng Guo, Sizhuo Yan, Lihong Zhi
We consider the problem of extending the classical S-lemma from commutative case to noncommutative cases. We show that a symmetric quadratic homogeneous matrix-valued polynomial is…