THE TRIANGULAR MODEL OF SEMI-SIMPLE L~*-ALGEBRA OF H-S OPERATORS

In this paper,some properties of semi-simple L-algebras are considered.At first,applying Cartan decomposition,the author constructs a family of nilpotentsubalgebras in a semi-simple L-algebra and proves that whole algebra can be spanned bythese subalgebras,their conjugations and Cartan subalgebras.Then,the author proves that every nonzero root vector of semi-simple L-algebra ofH-S operators is a finite rank operator and presents the triangular model of the algebra.Finally,non-Voltera property of the algebra is shown.

THE TRIANGULAR MODEL OF SEMI-SIMPLE $\[{L^*}\]$-ALGEBRA OF H-S OPERATORS

In this paper, some properties of semi-simple $\{L^*}\]$-algebras are considered. At first, applying Cartan decomposition, the author constructs a family of nilpotent subalgebras in a semi-simple $\{L^*}\]$-algebra and proves that whole algebra can be spanned by these subalgebras, their conjugations and Cartan subalgebras. Then, the author proves that every nonzero root vector of semi-simple $\{L^*}\]$-algebra of H-S operators is a finite rank operator and presents the triangular model of the algebra. Finally, non-Voltera property of the algebra is shown.