In mathematics, an algebra bundle is a fiber bundle whose fibers are algebras and local trivializations respect the algebra structure. It follows that...

In mathematics, a weak Lie algebra bundle ξ = ( ξ , p , X , θ ) {\displaystyle \xi =(\xi ,p,X,\theta )\,} is a vector bundle ξ {\displaystyle \xi \,} over...

calculation for algebraic geometry. For example, the fact that the canonical bundle is a negative multiple of the ample line bundle O ( 1 ) {\displaystyle...

In mathematics, the tensor algebra of a vector space V, denoted T(V) or T•(V), is the algebra of tensors on V (of any rank) with multiplication being the...

canonical bundle of a non-singular algebraic variety V {\displaystyle V} of dimension n {\displaystyle n} over a field is the line bundle Ω n = ω {\displaystyle...

adjoint bundle is a vector bundle naturally associated with any smooth principal bundle. The fibers of the adjoint bundle carry a Lie algebra structure...

Affine bundle Algebra bundle Characteristic class Covering map Equivariant bundle Fibered manifold Fibration Gauge theory Hopf bundle I-bundle Natural...

In mathematics, a distinctive feature of algebraic geometry is that some line bundles on a projective variety can be considered "positive", while others...

{\displaystyle X} (e.g. a topological space, manifold, or algebraic variety), which is then called a vector bundle over X {\displaystyle X} . The simplest example...

Lie algebroid, which is the vertical bundle of the source map restricted at the units. However, unlike Lie algebras, not every Lie algebroid arises from...

"square roots" of sections of vector bundles – in the case of the exterior algebra bundle of the cotangent bundle, they thus become "square roots" of differential...

Clifford bundle is an algebra bundle whose fibers have the structure of a Clifford algebra and whose local trivializations respect the algebra structure...

tangent bundle is a way of organising these. More formally, in algebraic topology and differential topology, a line bundle is defined as a vector bundle of...

In mathematics, vector bundles on algebraic curves may be studied as holomorphic vector bundles on compact Riemann surfaces, which is the classical approach...

sheaf) algebraic varieties or schemes. In the smooth case, any Riemannian metric or symplectic form gives an isomorphism between the cotangent bundle and...

Algebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics. Classically, an algebraic variety is defined as...

spectral triple. It is constructed from a smooth vector bundle E over M, e.g. the exterior algebra bundle. The Hilbert space L2(M, E) of square integrable sections...

in the case of nilpotent Lie groups. Adjoint bundle – Lie algebra bundle associated to any principal bundle by the adjoint representationPages displaying...

alternative descriptions of important structures in algebraic geometry such as moduli spaces of vector bundles and coherent sheaves. Gauge theory has its origins...

mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra with the additional structure...

Tautological bundles are constructed both in algebraic topology and in algebraic geometry. In algebraic geometry, the tautological line bundle (as invertible...

the theory of connections on a principal bundle as well as in the theory of Cartan connections. A Lie-algebra-valued differential k {\displaystyle k} -form...

Clifford algebras. The canonical example is a spinor bundle. In fact, on a Spin manifold, every Clifford module is obtained by twisting the spinor bundle. The...

In mathematics, the exterior algebra or Grassmann algebra of a vector space V {\displaystyle V} is an associative algebra that contains V , {\displaystyle...

and algebraic geometry, a stable principal bundle is a generalisation of the notion of a stable vector bundle to the setting of principal bundles. The...

This is a glossary of algebraic geometry. See also glossary of commutative algebra, glossary of classical algebraic geometry, and glossary of ring theory...

called Swan's theorem, relates the geometric notion of vector bundles to the algebraic concept of projective modules and gives rise to a common intuition...

transport on the bundle; that is, a way to "connect" or identify fibers over nearby points. A principal G-connection on a principal G-bundle P {\displaystyle...

principal bundle. The Riemann curvature tensor in Riemannian geometry can be considered as a special case. Let G be a Lie group with Lie algebra g {\displaystyle...

A tangent bundle is the collection of all of the tangent spaces for all points on a manifold, structured in a way that it forms a new manifold itself....