Unital associative pseudoalgebras and their representations

Theory of Finite Pseudoalgebras

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...

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...

compactifications and representations of transformation semigroups

this thesis deals essentially (but not from all aspects) with the extension of the notion of semigroup compactification and the construction of a general theory of semitopological nonaffine (affine) transformation semigroup compactifications. it determines those compactification which are universal with respect to some algebric or topological properties. as an application of the theory, it is i...

Identities of Conformal Algebras and Pseudoalgebras

For a given conformal algebra C, we write down the correspondence between identities of the coefficient algebra Coeff C and identities of C itself as of pseudoalgebra. In particular, we write down the defining relations of Jordan, alternative and Mal’cev conformal algebras, and show that the analogue of Artin’s Theorem does not hold for alternative conformal algebras. 1. Conformal algebras In t...