| dbo:abstract |
In mathematics, an exp algebra is a Hopf algebra Exp(G) constructed from an abelian group G, and is the universal ring R such that there is an exponential map from G to the group of the power series in R[[t]] with constant term 1. In other words the functor Exp from abelian groups to commutative rings is adjoint to the functor from commutative rings to abelian groups taking a ring to the group of formal power series with constant term 1. The definition of the exp ring of G is similar to that of the group ring Z[G] of G, which is the universal ring such that there is an exponential homomorphism from the group to its units. In particular there is a natural homomorphism from the group ring to a completion of the exp ring. However in general the Exp ring can be much larger than the group ring: for example, the group ring of the integers is the ring of Laurent polynomials in 1 variable, while the exp ring is a polynomial ring in countably many generators. (en) |
| dbo:wikiPageID |
42475707 (xsd:integer) |
| dbo:wikiPageLength |
3506 (xsd:nonNegativeInteger) |
| dbo:wikiPageRevisionID |
1115805271 (xsd:integer) |
| dbo:wikiPageWikiLink |
dbr:Ring_of_symmetric_functions dbr:Coproduct dbr:Commutative_ring dbr:Hopf_algebra dbr:Λ-ring dbr:Laurent_polynomial dbr:Formal_power_series dbr:Ring_(mathematics) dbr:Abelian_group dbc:Hopf_algebras dbr:Group_ring dbr:Universal_property dbr:Hopf_algebra_of_symmetric_functions |
| dbp:first |
Nadiya (en) Michiel (en) V. V. (en) |
| dbp:isbn |
978 (xsd:integer) |
| dbp:last |
Kirichenko (en) Hazewinkel (en) Gubareni (en) |
| dbp:mr |
2724822 (xsd:integer) |
| dbp:place |
Providence, RI (en) |
| dbp:publisher |
American Mathematical Society (en) |
| dbp:series |
Mathematical Surveys and Monographs (en) |
| dbp:title |
Algebras, rings and modules. Lie algebras and Hopf algebras (en) |
| dbp:volume |
168 (xsd:integer) |
| dbp:wikiPageUsesTemplate |
dbt:Citation dbt:Harvtxt dbt:Harvs |
| dbp:year |
2010 (xsd:integer) |
| dbp:zbl |
1211.160230 (xsd:double) |
| dct:subject |
dbc:Hopf_algebras |
| gold:hypernym |
dbr:Exp |
| rdf:type |
yago:Abstraction100002137 yago:Algebra106012726 yago:Cognition100023271 yago:Content105809192 yago:Discipline105996646 yago:KnowledgeDomain105999266 yago:Mathematics106000644 yago:PsychologicalFeature100023100 yago:PureMathematics106003682 yago:WikicatHopfAlgebras yago:Science105999797 |
| rdfs:comment |
In mathematics, an exp algebra is a Hopf algebra Exp(G) constructed from an abelian group G, and is the universal ring R such that there is an exponential map from G to the group of the power series in R[[t]] with constant term 1. In other words the functor Exp from abelian groups to commutative rings is adjoint to the functor from commutative rings to abelian groups taking a ring to the group of formal power series with constant term 1. (en) |
| rdfs:label |
Exp algebra (en) |
| owl:sameAs |
freebase:Exp algebra yago-res:Exp algebra wikidata:Exp algebra https://global.dbpedia.org/id/faLz |
| prov:wasDerivedFrom |
wikipedia-en:Exp_algebra?oldid=1115805271&ns=0 |
| foaf:isPrimaryTopicOf |
wikipedia-en:Exp_algebra |
| is dbo:wikiPageRedirects of |
dbr:Exp_ring |
| is dbo:wikiPageWikiLink of |
dbr:Exp_ring |
| is foaf:primaryTopic of |
wikipedia-en:Exp_algebra |