Source Algebras of p-Central Group Extensions

Central Extensions of Stephenson’s Algebras

This paper completes the classification of central extensions of three dimensional Artin-Schelter regular algebras to four dimensional Artin-Schelter regular algebras. Let A be an AS regular algebra of global dimension three and let D be an extension of A by a central graded element z, i.e. D/〈z〉 = A. If A is generated by elements of degree one, those algebras D which are again AS regular have ...

On Central Extensions of Preprojective Algebras

μiei), where μ = (μi) is a regular weight (for the root system attached to Q), and ei are the vertex idempotents in P . 1 It is shown in [ER] that the algebra A has nicer properties than the ordinary Gelfand-Ponomarev preprojective algebra A0 = A/(z) of Q; in particular, the deformed version A(λ) of A = A(0) is flat, while this is not the case for A0. The paper [ER] also shows that A is a Frobe...

Central Extensions of Some Lie Algebras

We consider three Lie algebras: Der C((t)), the Lie algebra of all derivations on the algebra C((t)) of formal Laurent series; the Lie algebra of all differential operators on C((t)); and the Lie algebra of all differential operators on C((t)) ⊗ Cn. We prove that each of these Lie algebras has an essentially unique nontrivial central extension. The Lie algebra of all derivations on the Laurent ...

Central Idempotents in Group Algebras

Central Extensions of the families of Quasi-unitary Lie algebras

The most general possible central extensions of two whole families of Lie algebras, which can be obtained by contracting the special pseudo-unitary algebras su(p, q) of the Cartan series Al and the pseudo-unitary algebras u(p, q), are completely determined and classified for arbitrary p, q. In addition to the su(p, q) and u(p, q) algebras, whose second cohomology group is well known to be trivi...