‎we consider the uniqueness problem of algebroid functions‎ ‎on an angular domain‎. ‎several theorems are established to extend the uniqueness theory of meromorphic functions to algebroid functions‎.

We introduce Courant 1-derivations, which describe a compatibility between algebroids and linear (1,1)-tensor fields lead to the notion of Courant-Nijenhuis algebroids. provide examples 1-derivations on exact show that holomorphic can be viewed as special types By considering Dirac structures, one recovers Dirac-Nijenhuis structures previously studied by authors (in case standard algebroid) obt...

Symmetric ordering and Weyl realizations for non-commutative quantum Minkowski spaces are reviewed. of Lie deformed corresponding star products, as well twist to realization coproduct momenta, presented. Drinfeld twists understood in Hopf algebroid sense also discussed. A few examples given. We show that the original Snyder space, there exists symmetric but no realization. Quadratic deformation...

Given a vector bundle $A\to M$ we study the geometry of graded manifolds $T^*[k]A[1]$, including their canonical symplectic structures, compatible Q-structures and Lagrangian Q-submanifolds. We relate these objects to classical such as higher Courant algebroids on $A\oplus\bigwedge^{k-1}A^*$ Dirac structures therein, semi-direct products Lie algebroid $A$ with coadjoint representations up homot...

We examine Lie (super)algebroids equipped with a homological section, i.e., an odd section that ‘self-commutes’, we refer to such algebroids as inner Q-algebroids: these provide natural examples of suitably “superised” Q-algebroids in the sense Mehta. Such are generalisation Q-manifolds and superalgebras element. Amongst other results, show that, via derived bracket formalism, space sections Q-...

Using the language of h-Hopf algebroids which was introduced by Etingof and Varchenko, we construct a dynamical quantum group, Fell(GL(n)), from Felder’s elliptic solution of the quantum dynamical Yang-Baxter equation with spectral parameter associated to the Lie algebra sln. First we apply the generalized FRST construction and obtain a bialgebroid Fell(M(n)). Then, analogues of the exterior al...

We study affine Jacobi structures on an affine bundle π : A→M . We prove that there is a one-toone correspondence between affine Jacobi structures on A and Lie algebroid structures on the vector bundle A = ⋃ p∈M Aff(Ap,R) of affine functionals. Some examples and applications, also for the linear case, are discussed. For a special type of affine Jacobi structures which are canonically exhibited ...