On Lie algebras in braided categories

• Autorzy: Bodo Pareigis
• Języki publikacji: EN

Abstrakty

EN

The category of group-graded modules over an abelian group $G$ is a monoidal category. For any bicharacter of $G$ this category becomes a braided monoidal category. We define the notion of a Lie algebra in this category generalizing the concepts of Lie super and Lie color algebras. Our Lie algebras have $n$-ary multiplications between various graded components. They possess universal enveloping algebras that are Hopf algebras in the given category. Their biproducts with the group ring are noncommutative noncocommutative Hopf algebras some of them known in the literature. Conversely the primitive elements of a Hopf algebra in the category form a Lie algebra in the above sense.

Słowa kluczowe

EN

braided category; universal enveloping algebra; braided Hopf algebra; graded Lie algebra

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1997
• Tom: 40
• Numer: 1
• Strony: 139-158

Daty

wydano

1997

Twórcy

autor

Bodo Pareigis

• Mathematisches Institut der Universität München, Theresienstr. 39, 80333 Munich, Germany

Bibliografia

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