We realize the current algebra of a Kac-Moody algebra as a quotient of a semi-direct product of the Kac-Moody Lie algebra and the free Lie algebra of the Kac-Moody algebra. We use this realization to study the representations of the current algebra. In particular we see that every ad-invariant ideal in the symmetric algebra of the Kac-Moody algebra gives rise in a canonical way to a representat...

To any manifold equipped with a higher degree closed form, one can associate an L∞-algebra of local observables that generalizes the Poisson algebra of a symplectic manifold. Here, by means of an explicit homotopy equivalence, we interpret this L∞-algebra in terms of infinitesimal autoequivalences of higher prequantum bundles. By truncating the connection data on the prequantum bundle, we produ...

Motivated by algebraic structures appearing in Rational Conformal Field Theory we study a construction associating to an algebra in a monoidal category a commutative algebra (full centre) in the monoidal centre of the monoidal category. We establish Morita invariance of this construction by extending it to module categories. As an example we treat the case of group-theoretical categories.

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.