This HTML5 document contains 61 embedded RDF statements represented using HTML+Microdata notation.

The embedded RDF content will be recognized by any processor of HTML5 Microdata.

Namespace Prefixes

PrefixIRI
dctermshttp://purl.org/dc/terms/
dbohttp://dbpedia.org/ontology/
foafhttp://xmlns.com/foaf/0.1/
n12https://global.dbpedia.org/id/
dbthttp://dbpedia.org/resource/Template:
rdfshttp://www.w3.org/2000/01/rdf-schema#
rdfhttp://www.w3.org/1999/02/22-rdf-syntax-ns#
owlhttp://www.w3.org/2002/07/owl#
wikipedia-enhttp://en.wikipedia.org/wiki/
dbphttp://dbpedia.org/property/
provhttp://www.w3.org/ns/prov#
dbchttp://dbpedia.org/resource/Category:
xsdhhttp://www.w3.org/2001/XMLSchema#
wikidatahttp://www.wikidata.org/entity/
dbrhttp://dbpedia.org/resource/

Statements

Subject Item
dbr:Morphic_word
dbo:wikiPageWikiLink
dbr:Hall_word
Subject Item
dbr:Monoid_factorisation
dbo:wikiPageWikiLink
dbr:Hall_word
Subject Item
dbr:Commutator_collecting_process
dbo:wikiPageWikiLink
dbr:Hall_word
Subject Item
dbr:Hall_word
rdfs:label
Hall word
rdfs:comment
In mathematics, in the areas of group theory and combinatorics, Hall words provide a unique monoid factorisation of the free monoid. They are also totally ordered, and thus provide a total order on the monoid. This is analogous to the better-known case of Lyndon words; in fact, the Lyndon words are a special case, and almost all properties possessed by Lyndon words carry over to Hall words. Hall words are in one-to-one correspondence with Hall trees. These are binary trees; taken together, they form the Hall set. This set is a particular totally ordered subset of a free non-associative algebra, that is, a free magma. In this form, the Hall trees provide a basis for free Lie algebras, and can be used to perform the commutations required by the Poincaré–Birkhoff–Witt theorem used in the cons
dcterms:subject
dbc:Formal_languages dbc:Combinatorics_on_words
dbo:wikiPageID
31782613
dbo:wikiPageRevisionID
1048560707
dbo:wikiPageWikiLink
dbr:Free_monoid dbr:Mathematics dbr:Philip_Hall dbr:Hall–Petresco_identity dbr:Universal_enveloping_algebra dbr:Binary_tree dbr:Chen–Fox–Lyndon_theorem dbr:Markov_odometer dbr:Free_Lie_algebra dbr:Kleene_star dbr:Lyndon_word dbr:Monoid_factorisation dbr:Dirichlet_convolution dbr:Lexicographic_order dbr:Wilhelm_Magnus dbr:Free_magma dbr:Free_group dbr:Group_theory dbr:Marshall_Hall_(mathematician) dbr:Circular_shift dbr:Poincaré–Birkhoff–Witt_theorem dbr:Commutator_collecting_process dbr:Necklace_polynomial dbr:Graded_Lie_algebra dbr:Ernst_Witt dbr:Sequence dbr:Möbius_function dbr:Commutator dbr:Totally_ordered dbr:Filtration_(mathematics) dbr:Term_rewriting_system dbc:Combinatorics_on_words dbc:Formal_languages dbr:Combinatorics dbr:Confluence_(abstract_rewriting) dbr:Lower_central_series
owl:sameAs
wikidata:Q104841625 n12:FQwEk
dbp:wikiPageUsesTemplate
dbt:Short_description
dbo:abstract
In mathematics, in the areas of group theory and combinatorics, Hall words provide a unique monoid factorisation of the free monoid. They are also totally ordered, and thus provide a total order on the monoid. This is analogous to the better-known case of Lyndon words; in fact, the Lyndon words are a special case, and almost all properties possessed by Lyndon words carry over to Hall words. Hall words are in one-to-one correspondence with Hall trees. These are binary trees; taken together, they form the Hall set. This set is a particular totally ordered subset of a free non-associative algebra, that is, a free magma. In this form, the Hall trees provide a basis for free Lie algebras, and can be used to perform the commutations required by the Poincaré–Birkhoff–Witt theorem used in the construction of a universal enveloping algebra. As such, this generalizes the same process when done with the Lyndon words. Hall trees can also be used to give a total order to the elements of a group, via the commutator collecting process, which is a special case of the general construction given below. It can be shown that Lazard sets coincide with Hall sets. The historical development runs in reverse order from the above description. The commutator collecting process was described first, in 1934, by Philip Hall and explored in 1937 by Wilhelm Magnus. Hall sets were introduced by Marshall Hall based on work of Philip Hall on groups. Subsequently, Wilhelm Magnus showed that they arise as the graded Lie algebra associated with the filtration on a free group given by the lower central series. This correspondence was motivated by commutator identities in group theory due to Philip Hall and Ernst Witt.
prov:wasDerivedFrom
wikipedia-en:Hall_word?oldid=1048560707&ns=0
dbo:wikiPageLength
15722
foaf:isPrimaryTopicOf
wikipedia-en:Hall_word
Subject Item
dbr:Universal_enveloping_algebra
dbo:wikiPageWikiLink
dbr:Hall_word
Subject Item
dbr:Philip_Hall
dbo:wikiPageWikiLink
dbr:Hall_word
Subject Item
dbr:Free_Lie_algebra
dbo:wikiPageWikiLink
dbr:Hall_word
Subject Item
dbr:Free_monoid
dbo:wikiPageWikiLink
dbr:Hall_word
Subject Item
dbr:Wilhelm_Magnus
dbo:wikiPageWikiLink
dbr:Hall_word
Subject Item
dbr:Lyndon_word
dbo:wikiPageWikiLink
dbr:Hall_word
Subject Item
dbr:Hall_set
dbo:wikiPageWikiLink
dbr:Hall_word
dbo:wikiPageRedirects
dbr:Hall_word
Subject Item
wikipedia-en:Hall_word
foaf:primaryTopic
dbr:Hall_word