Faster access than browser!Similarities between Killing form and Lie algebra
Killing form and Lie algebra have 14 things in common (in Unionpedia): Adjoint representation, Cartan's criterion, Field (mathematics), Lie group, Lie group–Lie algebra correspondence, Mathematics, Nilpotent Lie algebra, Semisimple Lie algebra, Simple Lie group, Special linear group, Special unitary group, Symmetric bilinear form, Trace (linear algebra), Wilhelm Killing.
Adjoint representation
In mathematics, the adjoint representation (or adjoint action) of a Lie group G is a way of representing the elements of the group as linear transformations of the group's Lie algebra, considered as a vector space.
Adjoint representation and Killing form · Adjoint representation and Lie algebra ·
Cartan's criterion
In mathematics, Cartan's criterion gives conditions for a Lie algebra in characteristic 0 to be solvable, which implies a related criterion for the Lie algebra to be semisimple.
Cartan's criterion and Killing form · Cartan's criterion and Lie algebra ·
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 Killing form · Field (mathematics) and Lie algebra ·
Lie group
In mathematics, a Lie group (pronounced "Lee") is a group that is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure.
Killing form and Lie group · Lie algebra and Lie group ·
Lie group–Lie algebra correspondence
In mathematics, Lie group–Lie algebra correspondence allows one to study Lie groups, which are geometric objects, in terms of Lie algebras, which are linear objects.
Killing form and Lie group–Lie algebra correspondence · Lie algebra and Lie group–Lie algebra correspondence ·
Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
Killing form and Mathematics · Lie algebra and Mathematics ·
Nilpotent Lie algebra
In mathematics, a Lie algebra is nilpotent if its lower central series eventually becomes zero.
Killing form and Nilpotent Lie algebra · Lie algebra and Nilpotent Lie algebra ·
Semisimple Lie algebra
In mathematics, a Lie algebra is semisimple if it is a direct sum of simple Lie algebras, i.e., non-abelian Lie algebras \mathfrak g whose only ideals are and \mathfrak g itself.
Killing form and Semisimple Lie algebra · Lie algebra and Semisimple Lie algebra ·
Simple Lie group
In group theory, a simple Lie group is a connected non-abelian Lie group G which does not have nontrivial connected normal subgroups.
Killing form and Simple Lie group · Lie algebra and Simple Lie group ·
Special linear group
In mathematics, the special linear group of degree n over a field F is the set of matrices with determinant 1, with the group operations of ordinary matrix multiplication and matrix inversion.
Killing form and Special linear group · Lie algebra and Special linear group ·
Special unitary group
In mathematics, the special unitary group of degree, denoted, is the Lie group of unitary matrices with determinant 1.
Killing form and Special unitary group · Lie algebra and Special unitary group ·
Symmetric bilinear form
A symmetric bilinear form on a vector space is a bilinear map from two copies of the vector space to the field of scalars such that the order of the two vectors does not affect the value of the map.
Killing form and Symmetric bilinear form · Lie algebra and Symmetric bilinear form ·
Trace (linear algebra)
In linear algebra, the trace of an n-by-n square matrix A is defined to be the sum of the elements on the main diagonal (the diagonal from the upper left to the lower right) of A, i.e., where aii denotes the entry on the ith row and ith column of A. The trace of a matrix is the sum of the (complex) eigenvalues, and it is invariant with respect to a change of basis.
Killing form and Trace (linear algebra) · Lie algebra and Trace (linear algebra) ·
Wilhelm Killing
Wilhelm Karl Joseph Killing (10 May 1847 – 11 February 1923) was a German mathematician who made important contributions to the theories of Lie algebras, Lie groups, and non-Euclidean geometry.
Killing form and Wilhelm Killing · Lie algebra and Wilhelm Killing ·
The list above answers the following questions
- What Killing form and Lie algebra have in common
- What are the similarities between Killing form and Lie algebra
Killing form and Lie algebra Comparison
Killing form has 32 relations, while Lie algebra has 117. As they have in common 14, the Jaccard index is 9.40% = 14 / (32 + 117).
References
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