Dosi, Anar01. Atılım University2024-10-062024-10-0620100379-40241841-77442-s2.0-77955022959https://hdl.handle.net/20.500.14411/8568The 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.eninfo:eu-repo/semantics/closedAccessNoncommutative holomorphic functions in elements of a Lie algebraformally-radical functionsnoncommutative parametrized complexesTaylor spectrumtransversalityArticle