Leibniz and the Amour Pur Controversy

Leibniz and the Infinite

The German universal genius Gottfried Wilhelm Leibniz was born in Leipzig on the 21st of June according to the Julian calendar (on the 1st of July according to the Gregorian calendar) 1646. From 1661 he studied at the universities of Leipzig and Jena. On February 22, 1667 he became Doctor of Laws at the university of Nürnberg-Altdorf. He declined the professorship that was offered to him at thi...

Cup-product for Leibniz Cohomology and Dual Leibniz Algebras

For any Lie algebra g there is a notion of Leibniz cohomology HL(g), which is defined like the classical Lie cohomology, but with the n-th tensor product g⊗n in place of the n-th exterior product Λ g. This Leibniz cohomology is defined on a larger class of algebras : the Leibniz algebras (cf. [L1], [L2]). A Leibniz algebra is a vector space equipped with a product satisfying a variation of the ...

The Leibniz notation on manifolds

which is extremely strange the first time one encounters it. After all, why not just write V (x, y) = ye1 − xe2 where e1 = (1, 0), e2 = (0, 1)? What do partial derivatives have to do with anything? (That was the question I asked.) However, if viewed in the right way, it is not so strange. For if a vector field V is given, then one natural thing that can be done with it is to differentiate a sca...

Leibniz — Beyond The Calculus

Leibniz Algebras and Lie Algebras

This paper concerns the algebraic structure of finite-dimensional complex Leibniz algebras. In particular, we introduce left central and symmetric Leibniz algebras, and study the poset of Lie subalgebras using an associative bilinear pairing taking values in the Leibniz kernel.