Planar Lyapunov Algebras

• 作者: Matej Mencinger Borut Zalar
• 来源期刊: 代数集刊（英文版）
• 年，卷（期）: 2020,（3）
• 页码范围: 433-446
• 页数: 14页
• 语种: 英文
• DOI: 10.1142/S1005386720000358

摘要

We study complex involutive algebras generated by a single nonselfadjoint idempotent and use them to construct a family of algebras,which we call planar Lyapunov algebras.As our main result,we prove that every 2-dimensional commutative real algebra whose homogeneous Riccati differential equation is stable at the origin must be isomorphic either to an algebra with zero multiplication or to some planar Lyapunov algebra.