Applications of a noncommutative Jacobian matrix

DOI10.1016/0022-4049(92)90083-RzbMath0746.16016MaRDI QIDQ1184034

Christophe Reutenauer

Publication date: 28 June 1992

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

zbMATH Keywords

free Lie algebrafree algebrainversion formulaJacobian matrixcontinuous automorphismscontinuous homomorphismelementary automorphismsfree power series ring

Mathematics Subject Classification ID

Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) (16S10) Automorphisms and endomorphisms (16W20) Identities, free Lie (super)algebras (17B01) Derivations, actions of Lie algebras (16W25)

Related Items (21)

Partial derivatives and endomorphisms of some relatively free Lie algebras ⋮ Unnamed Item ⋮ Obstructions to lifting automorphisms of free algebras ⋮ Automorphisms of free polynilpotent lie algebras ⋮ The Jacobian Conjecture, Together with Specht and Burnside-Type Problems ⋮ Primitive and almost primitive elements of Schreier varieties ⋮ Universal enveloping algebras and universal derivations of Poisson algebras ⋮ Subalgebras of free algebras ⋮ Wild automorphisms of nilpotent-by-abelian Lie algebras ⋮ Subalgebras of free leibniz algebras ⋮ Test Elements, Retracts and Automorphic Orbits of Free Algebras ⋮ An inverse function theorem for free associative algebras of rank two ⋮ On the Rank of an Element of a Free Lie Algebra ⋮ Automorphic orbits in free non-associative algebras ⋮ RECOGNIZING AUTOMORPHISMS OF THE FREE COLOR LIE SUPERALGEBRAS ⋮ VARIETIES OF METABELIAN LEIBNIZ ALGEBRAS ⋮ Primitive elements and automorphisms of free algebras of Schreier varieties ⋮ Test Sets and Test Rank of a Free Metabelian Lie Algebra ⋮ On isomorphism classes and invariants of a subclass of low-dimensional complex filiform Leibniz algebras ⋮ Left-symmetric algebras of derivations of free algebras ⋮ Free (rational) derivation

Cites Work

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• Über die Darstellung von implizit gegebenen Funktionen mittels Lie-Reihen und Verallgemeinerungen der Lagrangeschen Reihe
• Free differential calculus. I: Derivation in the free group ring. II: The isomerphism problem of groups. III: Subgroups
• A jacobian conjecture for free associative algebras
• An Inverse Function Theorem for Free Groups
• Subalgebras of Free Associative Algebras

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