Taylor Functional Calculus for Supernilpotent Lie Algebra of Operators

Abstract

The present work is motivated by J.L. Taylor's program on noncommutative holomorphic functional calculus within the Lie algebra framework. We propose a sheaf T-g of germs of formally-radical functions in elements of a finite dimensional nilpotent Lie algebra g and prove the functional calculus theorem for an operator family generating a supernilpotent Lie sub-algebra based upon the sheaf T-g. This calculus extends Taylor's holomorphic functional calculus for a mutually commuting operator family.