Maps preserving zeros of a polynomial
J. Alaminos, M. Bre\v{s}ar, \v{S}. \v{S}penko, A. R. Villena

TL;DR
This paper characterizes linear maps on matrix algebras that preserve the zero set of multilinear polynomials, extending understanding of algebraic structure preservation under such maps.
Contribution
It provides a solution for describing zero-preserving linear maps on matrix algebras for general multilinear polynomials under certain conditions.
Findings
Characterized zero-preserving maps for general polynomials on matrix algebras.
Extended results to specific polynomials on broader classes of algebras.
Identified technical conditions under which the preservation property holds.
Abstract
Let be an algebra and let be a multilinear polynomial in noncommuting indeterminates . We consider the problem of describing linear maps that preserve zeros of . Under certain technical restrictions we solve the problem for general polynomials in the case where . We also consider quite general algebras , but only for specific polynomials .
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Advanced Differential Equations and Dynamical Systems
