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- 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)
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- 3506 (xsd:nonNegativeInteger)
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- Nadiya (en)
- Michiel (en)
- V. V. (en)
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- Kirichenko (en)
- Hazewinkel (en)
- Gubareni (en)
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- American Mathematical Society (en)
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- Mathematical Surveys and Monographs (en)
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- Algebras, rings and modules.
Lie algebras and Hopf algebras (en)
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| rdfs:comment
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- 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)
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