Theory of Finite Pseudoalgebras

Irreducible Modules over Finite Simple Lie Pseudoalgebras I. Primitive Pseudoalgebras of Type W and S

One of the algebraic structures that has emerged recently in the study of the operator product expansions of chiral fields in conformal field theory is that of a Lie conformal algebra [K]. A Lie pseudoalgebra is a generalization of the notion of a Lie conformal algebra for which C[∂] is replaced by the universal enveloping algebra H of a finite-dimensional Lie algebra [BDK]. The finite (i.e., f...

Simple Finite Jordan Pseudoalgebras⋆

We consider the structure of JordanH-pseudoalgebras which are linearly finitely generated over a Hopf algebra H . There are two cases under consideration: H = U(h) and H = U(h)#C[Γ], where h is a finite-dimensional Lie algebra over C, Γ is an arbitrary group acting on U(h) by automorphisms. We construct an analogue of the Tits–Kantor–Koecher construction for finite Jordan pseudoalgebras and des...

Irreducible Modules over Finite Simple Lie Pseudoalgebras I. Primitive Pseudoalgebras of Type W and S Bojko Bakalov, Alessandro D’andrea, and Victor G. Kac

Lie Algebroids and Lie Pseudoalgebras

Lie algebroids and Lie pseudoalgebras arise from a wide variety of constructions in differential geometry; they have been introduced repeatedly into the geometry, physics and algebra literatures since the 1950s, under some 14 different terminologies. The first main part (Sections 2-5) of this survey describes the four principal classes of examples, emphazising that each arises by means of a gen...

Profunctor Semantics for Linear Logic

Linear logic is a sort of “resource-aware” logic underlying intuitionistic logic. Investigations into the proof theory of this logic typically revolve around proof nets, certain two-dimensional graphical representations of proofs. Where sequent calculus deductions enforce arbitrary distinctions between proofs and complicate these investigations, proof nets represent sequent calculus deductions ...