On Lie and associative duals

Non-Associative Local Lie Groups

A general method for constructing local Lie groups which are not contained in any global Lie group is described. These examples fail to satisfy the global associativity axiom which, by a theorem of Mal’cev, is necessary and sufficient for globalizability. Furthermore, we prove that every local Lie group can be characterized by such a covering construction, thereby generalizing Cartan’s global v...

0 On associative algebras with unity and Lie index 1

On Associative Algebras with Unity and Lie Index 1

On the Associative Homotopy Lie Algebras and the Wronskians

Representations of the Schlessinger–Stasheff’s associative homotopy Lie algebras in the spaces of higher–order differential operators are analyzed. The W transformations of chiral embeddings, related with the Toda equations, of complex curves into the Kähler manifolds are shown to be endowed with the homotopy Lie algebra structures. Extensions of the Wronskian determinants that preserve the pro...

Resolutions of Associative and Lie Algebras

Certain canonical resolutions are described for free associative and free Lie algebras in the category of non-associative algebras. These resolutions derive in both cases from geometric objects, which in turn reflect the combinatorics of suitable collections of leaf-labeled trees.