Faster access than browser!Similarities between E7 (mathematics) and E8 (mathematics)
E7 (mathematics) and E8 (mathematics) have 43 things in common (in Unionpedia): Algebraic group, ATLAS of Finite Groups, Cartan matrix, Cartan subalgebra, Cartan subgroup, Chevalley basis, Classification of finite simple groups, Compact space, Complex dimension, Dynkin diagram, E6 (mathematics), En (Lie algebra), F4 (mathematics), Finite field, Freudenthal magic square, Fundamental representation, G2 (mathematics), Galois cohomology, Gauge theory, Graduate Texts in Mathematics, Group of Lie type, Hans Freudenthal, Heterotic string theory, Isometry group, Jacques Tits, John C. Baez, Lang's theorem, Lie group, List of simple Lie groups, Mathematics, ..., Octonion, Perfect field, Root system, Schur multiplier, Simple group, Simple Lie group, Springer Science+Business Media, String theory, Supergravity, Symmetric space, University of Chicago Press, Weyl character formula, Weyl group. Expand index (13 more) »
Algebraic group
In algebraic geometry, an algebraic group (or group variety) is a group that is an algebraic variety, such that the multiplication and inversion operations are given by regular maps on the variety.
Algebraic group and E7 (mathematics) · Algebraic group and E8 (mathematics) ·
ATLAS of Finite Groups
The ATLAS of Finite Groups, often simply known as the ATLAS, is a group theory book by John Horton Conway, Robert Turner Curtis, Simon Phillips Norton, Richard Alan Parker and Robert Arnott Wilson (with computational assistance from J. G. Thackray), published in December 1985 by Oxford University Press and reprinted with corrections in 2003.
ATLAS of Finite Groups and E7 (mathematics) · ATLAS of Finite Groups and E8 (mathematics) ·
Cartan matrix
In mathematics, the term Cartan matrix has three meanings.
Cartan matrix and E7 (mathematics) · Cartan matrix and E8 (mathematics) ·
Cartan subalgebra
In mathematics, a Cartan subalgebra, often abbreviated as CSA, is a nilpotent subalgebra \mathfrak of a Lie algebra \mathfrak that is self-normalising (if \in \mathfrak for all X \in \mathfrak, then Y \in \mathfrak).
Cartan subalgebra and E7 (mathematics) · Cartan subalgebra and E8 (mathematics) ·
Cartan subgroup
In mathematics, a Cartan subgroup of a Lie group or algebraic group G is one of the subgroups whose Lie algebra is a Cartan subalgebra.
Cartan subgroup and E7 (mathematics) · Cartan subgroup and E8 (mathematics) ·
Chevalley basis
In mathematics, a Chevalley basis for a simple complex Lie algebra is a basis constructed by Claude Chevalley with the property that all structure constants are integers.
Chevalley basis and E7 (mathematics) · Chevalley basis and E8 (mathematics) ·
Classification of finite simple groups
In mathematics, the classification of the finite simple groups is a theorem stating that every finite simple group belongs to one of four broad classes described below.
Classification of finite simple groups and E7 (mathematics) · Classification of finite simple groups and E8 (mathematics) ·
Compact space
In mathematics, and more specifically in general topology, compactness is a property that generalizes the notion of a subset of Euclidean space being closed (that is, containing all its limit points) and bounded (that is, having all its points lie within some fixed distance of each other).
Compact space and E7 (mathematics) · Compact space and E8 (mathematics) ·
Complex dimension
In mathematics, complex dimension usually refers to the dimension of a complex manifold M, or a complex algebraic variety V. If the complex dimension is d, the real dimension will be 2d.
Complex dimension and E7 (mathematics) · Complex dimension and E8 (mathematics) ·
Dynkin diagram
In the mathematical field of Lie theory, a Dynkin diagram, named for Eugene Dynkin, is a type of graph with some edges doubled or tripled (drawn as a double or triple line).
Dynkin diagram and E7 (mathematics) · Dynkin diagram and E8 (mathematics) ·
E6 (mathematics)
In mathematics, E6 is the name of some closely related Lie groups, linear algebraic groups or their Lie algebras \mathfrak_6, all of which have dimension 78; the same notation E6 is used for the corresponding root lattice, which has rank 6.
E6 (mathematics) and E7 (mathematics) · E6 (mathematics) and E8 (mathematics) ·
En (Lie algebra)
In mathematics, especially in Lie theory, En is the Kac–Moody algebra whose Dynkin diagram is a bifurcating graph with three branches of length 1,2, and k, with k.
E7 (mathematics) and En (Lie algebra) · E8 (mathematics) and En (Lie algebra) ·
F4 (mathematics)
In mathematics, F4 is the name of a Lie group and also its Lie algebra f4.
E7 (mathematics) and F4 (mathematics) · E8 (mathematics) and F4 (mathematics) ·
Finite field
In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements.
E7 (mathematics) and Finite field · E8 (mathematics) and Finite field ·
Freudenthal magic square
In mathematics, the Freudenthal magic square (or Freudenthal–Tits magic square) is a construction relating several Lie algebras (and their associated Lie groups).
E7 (mathematics) and Freudenthal magic square · E8 (mathematics) and Freudenthal magic square ·
Fundamental representation
In representation theory of Lie groups and Lie algebras, a fundamental representation is an irreducible finite-dimensional representation of a semisimple Lie group or Lie algebra whose highest weight is a fundamental weight.
E7 (mathematics) and Fundamental representation · E8 (mathematics) and Fundamental representation ·
G2 (mathematics)
In mathematics, G2 is the name of three simple Lie groups (a complex form, a compact real form and a split real form), their Lie algebras \mathfrak_2, as well as some algebraic groups.
E7 (mathematics) and G2 (mathematics) · E8 (mathematics) and G2 (mathematics) ·
Galois cohomology
In mathematics, Galois cohomology is the study of the group cohomology of Galois modules, that is, the application of homological algebra to modules for Galois groups.
E7 (mathematics) and Galois cohomology · E8 (mathematics) and Galois cohomology ·
Gauge theory
In physics, a gauge theory is a type of field theory in which the Lagrangian is invariant under certain Lie groups of local transformations.
E7 (mathematics) and Gauge theory · E8 (mathematics) and Gauge theory ·
Graduate Texts in Mathematics
Graduate Texts in Mathematics (GTM) (ISSN 0072-5285) is a series of graduate-level textbooks in mathematics published by Springer-Verlag.
E7 (mathematics) and Graduate Texts in Mathematics · E8 (mathematics) and Graduate Texts in Mathematics ·
Group of Lie type
In mathematics, specifically in group theory, the phrase group of Lie type usually refers to finite groups that are closely related to the group of rational points of a reductive linear algebraic group with values in a finite field.
E7 (mathematics) and Group of Lie type · E8 (mathematics) and Group of Lie type ·
Hans Freudenthal
Hans Freudenthal (17 September 1905 – 13 October 1990) was a Jewish-German-born Dutch mathematician.
E7 (mathematics) and Hans Freudenthal · E8 (mathematics) and Hans Freudenthal ·
Heterotic string theory
In string theory, a heterotic string is a closed string (or loop) which is a hybrid ('heterotic') of a superstring and a bosonic string.
E7 (mathematics) and Heterotic string theory · E8 (mathematics) and Heterotic string theory ·
Isometry group
In mathematics, the isometry group of a metric space is the set of all bijective isometries (i.e. bijective, distance-preserving maps) from the metric space onto itself, with the function composition as group operation.
E7 (mathematics) and Isometry group · E8 (mathematics) and Isometry group ·
Jacques Tits
Jacques Tits (born 12 August 1930 in Uccle) is a Belgium-born French mathematician who works on group theory and incidence geometry, and who introduced Tits buildings, the Tits alternative, and the Tits group.
E7 (mathematics) and Jacques Tits · E8 (mathematics) and Jacques Tits ·
John C. Baez
John Carlos Baez (born June 12, 1961) is an American mathematical physicist and a professor of mathematics at the University of California, Riverside (UCR) in Riverside, California.
E7 (mathematics) and John C. Baez · E8 (mathematics) and John C. Baez ·
Lang's theorem
In algebraic geometry, Lang's theorem, introduced by Serge Lang, states: if G is a connected smooth algebraic group over a finite field \mathbf_q, then, writing \sigma: G \to G, \, x \mapsto x^q for the Frobenius, the morphism of varieties is surjective.
E7 (mathematics) and Lang's theorem · E8 (mathematics) and Lang's theorem ·
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.
E7 (mathematics) and Lie group · E8 (mathematics) and Lie group ·
List of simple Lie groups
In mathematics, the simple Lie groups were first classified by Wilhelm Killing and later perfected by Élie Cartan.
E7 (mathematics) and List of simple Lie groups · E8 (mathematics) and List of simple Lie groups ·
Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
E7 (mathematics) and Mathematics · E8 (mathematics) and Mathematics ·
Octonion
In mathematics, the octonions are a normed division algebra over the real numbers, usually represented by the capital letter O, using boldface O or blackboard bold \mathbb O. There are three lower-dimensional normed division algebras over the reals: the real numbers R themselves, the complex numbers C, and the quaternions H. The octonions have eight dimensions; twice the number of dimensions of the quaternions, of which they are an extension.
E7 (mathematics) and Octonion · E8 (mathematics) and Octonion ·
Perfect field
In algebra, a field k is said to be perfect if any one of the following equivalent conditions holds.
E7 (mathematics) and Perfect field · E8 (mathematics) and Perfect field ·
Root system
In mathematics, a root system is a configuration of vectors in a Euclidean space satisfying certain geometrical properties.
E7 (mathematics) and Root system · E8 (mathematics) and Root system ·
Schur multiplier
In mathematical group theory, the Schur multiplier or Schur multiplicator is the second homology group H2(G, Z) of a group G. It was introduced by in his work on projective representations.
E7 (mathematics) and Schur multiplier · E8 (mathematics) and Schur multiplier ·
Simple group
In mathematics, a simple group is a nontrivial group whose only normal subgroups are the trivial group and the group itself.
E7 (mathematics) and Simple group · E8 (mathematics) and Simple group ·
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.
E7 (mathematics) and Simple Lie group · E8 (mathematics) and Simple Lie group ·
Springer Science+Business Media
Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.
E7 (mathematics) and Springer Science+Business Media · E8 (mathematics) and Springer Science+Business Media ·
String theory
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings.
E7 (mathematics) and String theory · E8 (mathematics) and String theory ·
Supergravity
In theoretical physics, supergravity (supergravity theory; SUGRA for short) is a modern field theory that combines the principles of supersymmetry and general relativity where supersymmetry obeys locality; in contrast to non-gravitational supersymmetric theories such as the Minimal Supersymmetric Standard Model.
E7 (mathematics) and Supergravity · E8 (mathematics) and Supergravity ·
Symmetric space
In differential geometry, representation theory and harmonic analysis, a symmetric space is a pseudo-Riemannian manifold whose group of symmetries contains an inversion symmetry about every point.
E7 (mathematics) and Symmetric space · E8 (mathematics) and Symmetric space ·
University of Chicago Press
The University of Chicago Press is the largest and one of the oldest university presses in the United States.
E7 (mathematics) and University of Chicago Press · E8 (mathematics) and University of Chicago Press ·
Weyl character formula
In mathematics, the Weyl character formula in representation theory describes the characters of irreducible representations of compact Lie groups in terms of their highest weights.
E7 (mathematics) and Weyl character formula · E8 (mathematics) and Weyl character formula ·
Weyl group
In mathematics, in particular the theory of Lie algebras, the Weyl group of a root system Φ is a subgroup of the isometry group of the root system.
E7 (mathematics) and Weyl group · E8 (mathematics) and Weyl group ·
The list above answers the following questions
- What E7 (mathematics) and E8 (mathematics) have in common
- What are the similarities between E7 (mathematics) and E8 (mathematics)
E7 (mathematics) and E8 (mathematics) Comparison
E7 (mathematics) has 59 relations, while E8 (mathematics) has 120. As they have in common 43, the Jaccard index is 24.02% = 43 / (59 + 120).
References
This article shows the relationship between E7 (mathematics) and E8 (mathematics). To access each article from which the information was extracted, please visit:
