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Statements

Subject Item
dbr:Exp_algebra
rdf:type
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rdfs:label
Exp algebra
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.
dct:subject
dbc:Hopf_algebras
dbo:wikiPageID
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dbo:wikiPageRevisionID
1115805271
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freebase:m.010fbxy1 n15:faLz yago-res:Exp_algebra wikidata:Q17012869
dbp:zbl
1211.16023
dbp:wikiPageUsesTemplate
dbt:Citation dbt:Harvtxt dbt:Harvs
dbp:mr
2724822
dbp:first
Nadiya Michiel V. V.
dbp:isbn
978
dbp:last
Gubareni Hazewinkel Kirichenko
dbp:place
Providence, RI
dbp:publisher
American Mathematical Society
dbp:series
Mathematical Surveys and Monographs
dbp:title
Algebras, rings and modules. Lie algebras and Hopf algebras
dbp:volume
168
dbp:year
2010
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.
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dbr:Exp
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