Quasi-derivations and QD-algebroids
نویسنده
چکیده
Axioms of Lie algebroid are discussed. In particular, it is shown that a Lie QD-algebroid (i.e. a Lie algebra bracket on the C∞(M)-module E of sections of a vector bundle E over a manifold M which satisfies [X, fY ] = f [X, Y ] + A(X,f)Y for all X, Y ∈ E , f ∈ C∞(M), and for certain A(X,f) ∈ C∞(M)) is a Lie algebroid if rank(E) > 1, and is a local Lie algebra in the sense of Kirillov if E is a line bundle. Under a weak condition also the skew-symmetry of the bracket is relaxed.
منابع مشابه
Quasi-derivations and quasi-algebroids
Axioms of Lie algebroid are discussed. In particular, it is shown that a Lie quasi-algebroid (i.e. a Lie algebra bracket on the C∞(M)-module E of sections of a vector bundle E over a manifold M which satisfies [X, fY ] = f [X, Y ] + A(X,f)Y for all X, Y ∈ E , f ∈ C∞(M), and for certain A(X,f) ∈ C∞(M)) is a Lie algebroid if rank(E) > 1, and is a local Lie algebra in the sense of Kirillov if E is...
متن کاملQuasi-Poisson structures as Dirac structures
We show that quasi-Poisson structures can be identified with Dirac structures in suitable Courant algebroids. This provides a geometric way to construct Lie algebroids associated with quasi-Poisson spaces.
متن کاملMorita Theory for Hopf Algebroids and Presheaves of Groupoids
Comodules over Hopf algebroids are of central importance in algebraic topology. It is well-known that a Hopf algebroid is the same thing as a presheaf of groupoids on Aff , the opposite category of commutative rings. We show in this paper that a comodule is the same thing as a quasi-coherent sheaf over this presheaf of groupoids. We prove the general theorem that internal equivalences of preshe...
متن کاملDerivations of quasi *-algebras
The spatiality of derivations of quasi *-algebras is investigated by means of representation theory. Moreover, in view of physical applications, the spatiality of the limit of a family of spatial derivations is considered.
متن کاملError analysis for a non-standard class of differential quasi-interpolants
Given a B-spline M on R, s≥ 1 we consider a classical discrete quasi-interpolant Qd written in the form Qdf = ∑ i∈Zs f (i)L(· − i), where L(x) :=∑ j∈JcjM(x− j) for some finite subset J ⊂ Z and cj ∈R. This fundamental function is determined to produce a quasi-interpolation operator exact on the space of polynomials of maximal total degree included in the space spanned by the integer translates o...
متن کامل