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-dimen...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.展开更多
基金financial support from the Slovenian Research Agency(research core funding No.Pl-0288)the project Algebraic Methods for the Application of Differential Equations(No.N1-0063).
文摘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.
