mathematics, an algebroid function is a solution of an algebraic equation whose coefficients are analytic functions. So y(z) is an algebroid function if it satisfies...

In mathematics, R-algebroids are constructed starting from groupoids. These are more abstract concepts than the Lie algebroids that play a similar role...

(R = ∞). Subsequent generalizations extended Nevanlinna theory to algebroid functions, holomorphic curves, holomorphic maps between complex manifolds of...

In mathematics, a Lie algebroid is a vector bundle A → M {\displaystyle A\rightarrow M} together with a Lie bracket on its space of sections Γ ( A ) {\displaystyle...

a Courant algebroid is a vector bundle together with an inner product and a compatible bracket more general than that of a Lie algebroid. It is named...

employed in symplectic geometry, such as the theory of Lie groupoids and algebroids. Moreover, there are natural examples of structures which should be "morally"...

Fonctions et variétés algebroïdes, d'après F. Hirzebruch (algebroid functions, algebroid varieties) Robert Pallu de la Barrière, L'existence de sous-espaces...

compatible Lie algebroids defined on dual vector bundles. Lie bialgebroids are the vector bundle version of Lie bialgebras. A Lie algebroid consists of a...

groups and Lie algebras, Lie groupoids are the global counterparts of Lie algebroids. Lie groupoids were introduced by Charles Ehresmann under the name differentiable...

contributions to weak Hopf algebras are to be found in as well as See Hopf algebroid Groups can be axiomatized by the same diagrams (equivalently, operations)...

space Invariant theory Lie derivative Darboux derivative Lie groupoid Lie algebroid Lattice (group) Lattice (discrete subgroup) Frieze group Wallpaper group...

of the Lie algebroid. The distribution/foliation is regular if and only if ρ {\displaystyle \rho } has constant rank, i.e. the Lie algebroid is regular...

algebraic differential equations which have transcendental meromorphic or algebroid solutions. Theorem (1913). If the differential equation d w d z = R (...

Tannaka–Krein duality), in its groupoid algebra or in the commutative Hopf algebroid of functions on the groupoid. Thus formalisms trying to capture quantum groupoids...

These last objects can be also studied in terms of their associated Lie algebroids, in analogy to the relation between Lie groups and Lie algebras. Groupoids...

a-Beltrán, Dennise; Vallejo, José A.; Vorobjev, Yuriĭ (2012). "On Lie Algebroids and Poisson Algebras". Symmetry, Integrability and Geometry: Methods and...

Jacobi identity and so it does not define a Lie algebroid, in addition it fails to satisfy the Lie algebroid condition on the anchor map. Instead it defines...

org/nlab/show/image (Definition 3.1 and Remarks 3.2) in Gabriella Böhm, Hopf algebroids, in Handbook of Algebra (2008) arXiv:0805.3806 paragraph 2-14 at page...

The main areas of his research were the theory of Banach groupoids and algebroids related to the structure of W*-algebras, quantization of physical systems...

apply the implicit function theorem if it were true in algebraic geometry (but it isn't — implicit algebraic functions are called algebroid in older literature)...

vector bundles and de Rham differential of forms. Beside Lie algebroids, also Courant algebroids start playing a more important role. A Lie group is a group...

[X,Y]} . This turns the vector fields with the Lie bracket into a Lie algebroid. Vanishing of the Lie bracket of X {\displaystyle X} and Y {\displaystyle...

extended to quantum supergroups, quantum groupoids and their dual Hopf algebroids. In Pontryagin duality theory for locally compact commutative groups,...

tensor associated to a given pseudo-Riemannian metric Add structure of Lie algebroid to modules of vector fields (classes VectorFieldModule and VectorFieldFreeModule):...

P. and Ramazan B., Quantization of Poisson algebras associated to Lie algebroids, in Proc. Conf. on Groupoids in Physics, Analysis and Geometry(Boulder...

dg]=d\{f,g\}} for the Lie algebroid bracket of T ∗ M {\displaystyle T^{*}M} on exact 1-forms via the Poisson bracket of functions. In 1977 Lichnerowicz introduced...

comodules over Hopf-algebroids to construct algebraic models of gerbes over affine or projective stacks (projectivity if a graded Hopf-algebroid is used). In...

planes), Roger Bielawski (Berry–Robbins problem), Howard Donnelly (L-functions), Vladimir G. Drinfeld (instantons), Johan L. Dupont (singularities of...

= Mod(Vop)coop. Quantum categories were introduced to generalize Hopf algebroids and groupoids. A quantum groupoid is a Hopf algebra with several objects...

{\displaystyle {\mathcal {C(O)}}} or, equivalently, the Lie algebroid complex of the Lie algebroid C ( O ) {\displaystyle {\mathcal {C(O)}}} . Then the complex...