engleski

Toward integration of Lie algebras in Loday–Pirashvili category

It is well known that the category of Leibniz algebras embeds into the category of Lie algebras in the symmetric monoidal category of linear maps with so called infinitesimal tensor product, so called Loday- Pirashvili (LP) category. In characteristics zero, an analogue of Ado’s theorem holds for Lie algebras in LP category, hence a program of integration of such Lie algebras mainly depends on the resolution of the case of (an LP generalization of) matrix Lie algebras, hence the quest for matrix LP groups and the study of their infinitesimal geometry. I came across candidate internal bialgebras in LP category for the matrix LP groups ; while the study of invariant differential operators in this context is started with toy examples, and the calculation of Matija Bašić of an internal analogue of Weyl algebra, which shows combinatorially interesting new analogues of derivations.

Leibniz algebra; Loday-Pirashvili tensor category; Lie integration; bialgebra; internal Weyl algebra

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