Introduction For this course you need a very good understanding of linear algebra; a good knowledge of group theory and the representation theory of finite groups will also help. The main sources for these notes are the books [6] and [8]. We give complete proofs of all statements with the exception of the conjugacy of Cartan subgroups, the uniqueness theorem for semisimple Lie algebras, and the...

A basic problem in the theory of Lie algebra extensions concerns a given homomorphism x of a Lie algebra L into the Lie algebra of outer derivations of a Lie algebra B . In analogy with the theory of group extensions, Mori and HochschiId developed the concept of an obstruction to x being the homomorphism defined by some Lie algebra extension of B by L . This note considers an alternative approa...

The Kontsevich integral of a knot K lies in an algebra of diagrams Ac(S ). This algebra is (up to completion) a symmetric algebra of a graded module P , where P is the set of primitive elements of Ac(S ). The elements of P are represented by S-diagrams K such that the complement of the circle in K is connected and non empty. On the other hand there is an isomorphism from ⊕Bn to Ac(S ), where Bn...

An infinite-dimensional Lie Algebra is proposed which includes, in its subalgebras and limits, most Lie Algebras routinely utilized in physics. It relies on the finite oscillator Lie group, and appears applicable to twisted noncommutative QFT and CFT.

Abstract We prove two theorems about the Malcev Lie algebra associated to Torelli group of a surface genus g : Stably, it is Koszul and kernel Johnson homomorphism consists only trivial $\mathrm {Sp}_{2g}(\mathbb {Z})$ -representations lying in centre.

We construct an universal enveloping algebra associated to the ternary extension of Lie (super)algebras called Lie algebra of order three. A Poincaré-Birkhoff-Witt theorem is proven is this context. It this then shown that this universal enveloping algebra can be endowed with a structure of Hopf algebra. The study of the dual of the universal enveloping algebra enables to define the parameters ...