This paper is a natural extension of the previous note [Ar2]. Semiinfinite cohomology of Tate Lie algebra was defined in that note in terms of some duality resembling Koszul duality. The language of differential graded Lie algebroids was the main technical tool of the note. The present note is devoted to globalization of the main construction from [Ar2] in the following sense. The setup in [Ar2...

We study Lie algebra prederivations. A Lie algebra admitting a non-singular prederivation is nilpotent. We classify filiform Lie algebras admitting a non-singular prederivation but no non-singular derivation. We prove that any 4-step nilpotent Lie algebra admits a non-singular prederivation.

Let g be a Lie algebra over a field F of characteristic zero, let C be a certain tensor category of representations of g, and C a certain category of duals. By a Tannaka reconstruction we associate to C and C a monoid M with a coordinate ring of matrix coefficients F [M ] (which has in general no natural coalgebra structure), as well as a Lie algebra Lie(M). The monoid M and the Lie algebra Lie...

This paper describes progress made in context with the construction of a general library of Lie algebra algorithms, called ELIAS (Eindhoven LIe Algebra System), within the computer algebra package GAP. A first sketch of the package can be found in Cohen and de Graaf[1]. Since then, in a collaborative effort with G. Ivanyos, the authors have continued to develop algorithms which were implemented...

This paper describes progress made in context with the construction of a general library of Lie algebra algorithms, called ELIAS (Eindhoven LIe Algebra System), within the computer algebra package GAP. A first sketch of the package can be found in Cohen and de Graaf[1]. Since then, in a collaborative effort with G. Ivanyos, the authors have continued to develop algorithms which were implemented...