An Entity of Type : yago:WikicatLieGroups, within Data Space : dbpedia.org associated with source document(s)

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 used these bases to construct analogues of Lie groups over finite fields, called Chevalley groups. The Chevalley basis is the Cartan-Weyl basis, but with a different normalization. The generators of a Lie group are split into the generators H and E indexed by simple roots and their negatives . The Cartan-Weyl basis may be written as Defining the dual root or coroot of as One may perform a change of basis to define if then

AttributesValues
rdf:type
rdfs:label
• Chevalley basis
rdfs:comment
• 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 used these bases to construct analogues of Lie groups over finite fields, called Chevalley groups. The Chevalley basis is the Cartan-Weyl basis, but with a different normalization. The generators of a Lie group are split into the generators H and E indexed by simple roots and their negatives . The Cartan-Weyl basis may be written as Defining the dual root or coroot of as One may perform a change of basis to define if then
sameAs
dct:subject
Wikipage page ID
Wikipage revision ID
Link from a Wikipage to another Wikipage
foaf:isPrimaryTopicOf
prov:wasDerivedFrom
has abstract
• 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 used these bases to construct analogues of Lie groups over finite fields, called Chevalley groups. The Chevalley basis is the Cartan-Weyl basis, but with a different normalization. The generators of a Lie group are split into the generators H and E indexed by simple roots and their negatives . The Cartan-Weyl basis may be written as Defining the dual root or coroot of as One may perform a change of basis to define The Cartan integers are The resulting relations among the generators are the following: where in the last relation is the greatest positive integer such that is a root and we consider if is not a root. For determining the sign in the last relation one fixes an ordering of roots which respects addition, i.e., if then provided that all four are roots. We then call an extraspecial pair of roots if they are both positive and is minimal among all that occur in pairs of positive roots satisfying . The sign in the last relation can be chosen arbitrarily whenever is an extraspecial pair of roots. This then determines the signs for all remaining pairs of roots.
http://purl.org/voc/vrank#hasRank
is Link from a Wikipage to another Wikipage of
is foaf:primaryTopic of
Faceted Search & Find service v1.17_git21 as of Mar 09 2019

Alternative Linked Data Documents: iSPARQL | ODE     Content Formats:       RDF       ODATA       Microdata      About

OpenLink Virtuoso version 07.20.3230 as of May 1 2019, on Linux (x86_64-generic-linux-glibc25), Single-Server Edition (61 GB total memory)