Faster access than browser!Similarities between Lie algebra and Vector space
Lie algebra and Vector space have 24 things in common (in Unionpedia): Abelian group, Anticommutativity, Associative property, Bilinear map, Commutator, Cross product, Differentiable manifold, Endomorphism, Euclidean space, Euclidean vector, Field (mathematics), Group (mathematics), Homeomorphism, Isomorphism theorems, Jacobi identity, Linear map, Mathematics, Module (mathematics), Quantum mechanics, Representation theory, Ring (mathematics), Scalar (mathematics), Smoothness, Vector field.
Abelian group
In abstract algebra, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written.
Abelian group and Lie algebra · Abelian group and Vector space ·
Anticommutativity
In mathematics, anticommutativity is a specific property of some non-commutative operations.
Anticommutativity and Lie algebra · Anticommutativity and Vector space ·
Associative property
In mathematics, the associative property is a property of some binary operations.
Associative property and Lie algebra · Associative property and Vector space ·
Bilinear map
In mathematics, a bilinear map is a function combining elements of two vector spaces to yield an element of a third vector space, and is linear in each of its arguments.
Bilinear map and Lie algebra · Bilinear map and Vector space ·
Commutator
In mathematics, the commutator gives an indication of the extent to which a certain binary operation fails to be commutative.
Commutator and Lie algebra · Commutator and Vector space ·
Cross product
In mathematics and vector algebra, the cross product or vector product (occasionally directed area product to emphasize the geometric significance) is a binary operation on two vectors in three-dimensional space \left(\mathbb^3\right) and is denoted by the symbol \times.
Cross product and Lie algebra · Cross product and Vector space ·
Differentiable manifold
In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a linear space to allow one to do calculus.
Differentiable manifold and Lie algebra · Differentiable manifold and Vector space ·
Endomorphism
In mathematics, an endomorphism is a morphism (or homomorphism) from a mathematical object to itself.
Endomorphism and Lie algebra · Endomorphism and Vector space ·
Euclidean space
In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.
Euclidean space and Lie algebra · Euclidean space and Vector space ·
Euclidean vector
In mathematics, physics, and engineering, a Euclidean vector (sometimes called a geometric or spatial vector, or—as here—simply a vector) is a geometric object that has magnitude (or length) and direction.
Euclidean vector and Lie algebra · Euclidean vector and Vector space ·
Field (mathematics)
In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined, and behave as when they are applied to rational and real numbers.
Field (mathematics) and Lie algebra · Field (mathematics) and Vector space ·
Group (mathematics)
In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element and that satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility.
Group (mathematics) and Lie algebra · Group (mathematics) and Vector space ·
Homeomorphism
In the mathematical field of topology, a homeomorphism or topological isomorphism or bi continuous function is a continuous function between topological spaces that has a continuous inverse function.
Homeomorphism and Lie algebra · Homeomorphism and Vector space ·
Isomorphism theorems
In mathematics, specifically abstract algebra, the isomorphism theorems are three theorems that describe the relationship between quotients, homomorphisms, and subobjects.
Isomorphism theorems and Lie algebra · Isomorphism theorems and Vector space ·
Jacobi identity
In mathematics the Jacobi identity is a property of a binary operation which describes how the order of evaluation (the placement of parentheses in a multiple product) affects the result of the operation.
Jacobi identity and Lie algebra · Jacobi identity and Vector space ·
Linear map
In mathematics, a linear map (also called a linear mapping, linear transformation or, in some contexts, linear function) is a mapping between two modules (including vector spaces) that preserves (in the sense defined below) the operations of addition and scalar multiplication.
Lie algebra and Linear map · Linear map and Vector space ·
Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
Lie algebra and Mathematics · Mathematics and Vector space ·
Module (mathematics)
In mathematics, a module is one of the fundamental algebraic structures used in abstract algebra.
Lie algebra and Module (mathematics) · Module (mathematics) and Vector space ·
Quantum mechanics
Quantum mechanics (QM; also known as quantum physics, quantum theory, the wave mechanical model, or matrix mechanics), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.
Lie algebra and Quantum mechanics · Quantum mechanics and Vector space ·
Representation theory
Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures.
Lie algebra and Representation theory · Representation theory and Vector space ·
Ring (mathematics)
In mathematics, a ring is one of the fundamental algebraic structures used in abstract algebra.
Lie algebra and Ring (mathematics) · Ring (mathematics) and Vector space ·
Scalar (mathematics)
A scalar is an element of a field which is used to define a vector space.
Lie algebra and Scalar (mathematics) · Scalar (mathematics) and Vector space ·
Smoothness
In mathematical analysis, the smoothness of a function is a property measured by the number of derivatives it has that are continuous.
Lie algebra and Smoothness · Smoothness and Vector space ·
Vector field
In vector calculus and physics, a vector field is an assignment of a vector to each point in a subset of space.
Lie algebra and Vector field · Vector field and Vector space ·
The list above answers the following questions
- What Lie algebra and Vector space have in common
- What are the similarities between Lie algebra and Vector space
Lie algebra and Vector space Comparison
Lie algebra has 117 relations, while Vector space has 341. As they have in common 24, the Jaccard index is 5.24% = 24 / (117 + 341).
References
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