Smooth algebra information

In algebra, a commutative k-algebra A is said to be 0-smooth if it satisfies the following lifting property: given a k-algebra C, an ideal N of C whose...

In algebraic geometry, a smooth scheme over a field is a scheme which is well approximated by affine space near any point. Smoothness is one way of making...

an algebraic variety that is not singular is said to be regular. An algebraic variety that has no singular point is said to be non-singular or smooth. A...

. Lie algebras are closely related to Lie groups, which are groups that are also smooth manifolds: every Lie group gives rise to a Lie algebra, which...

topology Smooth manifold, a differentiable manifold for which all the transition maps are smooth functions Smooth algebraic variety, an algebraic variety...

+x_{n}^{2}-1=0} defines an algebraic hypersurface of dimension n − 1 in the Euclidean space of dimension n. This hypersurface is also a smooth manifold, and is...

derivations of the algebra of smooth functions on M. This "algebraization" of a manifold (replacing a geometric object with an algebra) leads to the notion...

on any smooth manifold M can be thought of as derivations X of the ring of smooth functions on the manifold, and therefore form a Lie algebra under the...

of smooth functions instead such a construction becomes possible, as demonstrated first by Colombeau. As a mathematical tool, Colombeau algebras can...

Heyting algebra Hopf algebra Non-associative algebra Outline of algebra Relational algebra Sigma-algebra Symmetric algebra T-algebra Tensor algebra When...

In algebraic geometry, the smooth completion (or smooth compactification) of a smooth affine algebraic curve X is a complete smooth algebraic curve which...

If one can show that a collection of interesting objects (e.g., the smooth algebraic curves of a fixed genus) can be given the structure of a geometric...

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

In algebraic geometry, a morphism f : X → S {\displaystyle f:X\to S} between schemes is said to be smooth if (i) it is locally of finite presentation (ii)...

universal algebra, an algebraic structure is called an algebra; this term may be ambiguous, since, in other contexts, an algebra is an algebraic structure...

{\mathfrak {g}}} is a Lie algebra, the tensor product of g {\displaystyle {\mathfrak {g}}} with C∞(S1), the algebra of (complex) smooth functions over the circle...

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

help in solving these problems. Every algebraic curve may be uniquely decomposed into a finite number of smooth monotone arcs (also called branches) sometimes...

mathematics, real algebraic geometry is the sub-branch of algebraic geometry studying real algebraic sets, i.e. real-number solutions to algebraic equations with...

concerning smooth algebras, and more general non-flat algebras A {\displaystyle A} ; but, the second is a direct generalization of the first. In the smooth case...

In algebraic geometry and commutative algebra, a ring homomorphism f : A → B {\displaystyle f:A\to B} is called formally smooth (from French: Formellement...

element of a Lie group forms a Lie algebra, the tangent space of the identity of a smooth Moufang loop forms a Malcev algebra. Moreover, just as a Lie group...

so of dimension four as a smooth manifold. The theory of algebraic surfaces is much more complicated than that of algebraic curves (including the compact...

below. Poisson algebras occur in various settings. The space of real-valued smooth functions over a symplectic manifold forms a Poisson algebra. On a symplectic...

tangent and secant lines of any non-planar smooth algebraic curve is three-dimensional. Further, any smooth algebraic variety with the property that every length...

In mathematics, a vertex operator algebra (VOA) is an algebraic structure that plays an important role in two-dimensional conformal field theory and string...