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 diagrams arise...

In geometry, a Coxeter–Dynkin diagram (or Coxeter diagram, Coxeter graph) is a graph with numerically labeled edges (called branches) representing a Coxeter...

algebras, and Markov processes. The Dynkin diagram, the Dynkin system, and Dynkin's lemma are named after him. Dynkin was born into a Jewish family, living...

Aleksandr Dynkin (born 1948), Russian economist Eugene Dynkin (1924–2014), Soviet and American mathematician known for Dynkin diagram Coxeter–Dynkin diagram Dynkin...

are applied. Further, the classification scheme for root systems, by Dynkin diagrams, occurs in parts of mathematics with no overt connection to Lie theory...

field. In particular, the simple algebraic groups are classified by Dynkin diagrams, as in the theory of compact Lie groups or complex semisimple Lie algebras...

mathematical study of Lie algebras and Lie groups, a Satake diagram is a generalization of a Dynkin diagram introduced by Satake (1960, p.109) whose configurations...

obtain other Dynkin diagrams and these correspond to twisted affine Lie algebras. The attachment of an extra node to the Dynkin diagram of the corresponding...

(over a perfect field k) by the set H1(k,Aut(E8)), which, because the Dynkin diagram of E8 (see below) has no automorphisms, coincides with H1(k,E8). Over...

A diagram is a symbolic representation of information using visualization techniques. Diagrams have been used since prehistoric times on walls of caves...

It has a non-algebraic double cover that is simply connected. The Dynkin diagram for G2 is given by . Its Cartan matrix is: [ 2 − 3 − 1 2 ] {\displaystyle...

figure. Its Coxeter symbol is 421, describing its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of the 4-node sequences, . The rectified...

vector spaces. Most commonly, it describes those special features of the Dynkin diagram D4 and the associated Lie group Spin(8), the double cover of 8-dimensional...

vertices). Its Coxeter symbol is 122, describing its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of the 1-node sequence. There are two...

of E8. In older books and papers, F4 is sometimes denoted by E4. The Dynkin diagram for F4 is: . Its Weyl/Coxeter group G = W(F4) is the symmetry group...

(over a perfect field k) by the set H1(k, Aut(E6)) which, because the Dynkin diagram of E6 (see below) has automorphism group Z/2Z, maps to H1(k, Z/2Z) =...

figure. Its Coxeter symbol is 321, describing its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of one of the 3-node sequences. The rectified...

bifurcated Coxeter-Dynkin diagram of lengths 6,2,1. There are 1023 unique E10 honeycombs by all combinations of its Coxeter-Dynkin diagram. There are no regular...

are exactly 24 Dynkin diagrams with these properties, and there turns out to be a unique Niemeier lattice for each of these Dynkin diagrams. The complete...

polytope. Its Coxeter symbol is 221, describing its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of one of the 2-node sequences. He also...

polytopes, generated by marking one or more nodes of the D10 Coxeter-Dynkin diagram. Of these, 511 (2×256−1) are repeated from the B10 family and 256 are...

creates a maximum number of facets. It is represented in a Coxeter–Dynkin diagram with all nodes ringed. It is a shortcut term which has a different meaning...

generalized Dynkin diagrams. When small primes are present, some exotic examples, such as a triangle, occur (see also the Figure of a rank 3 Dankin diagram). Meanwhile...

the structure of the associated Dynkin diagram. In this way one may identify the automorphism group of the Dynkin diagram of G with a subgroup of Out(G)...

listed so that their corresponding nodes in the Dynkin diagram are ordered from left to right (in the diagram depicted above) with the side node last. An...

group. Its Coxeter symbol is 231, describing its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of the 2-node branch. The rectified 231...

where certain kinds of objects are in correspondence with simply laced Dynkin diagrams. The question of giving a common origin to these classifications, rather...

{\displaystyle \beta } are in Δ {\displaystyle \Delta } , then the Dynkin diagram for Φ {\displaystyle \Phi } relative to the base Δ {\displaystyle \Delta...

group. Its Coxeter symbol is 142, describing its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of the 1-node sequences. The rectified...

group. Its Coxeter symbol is 132, describing its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of one of the 1-node sequences. The rectified...