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Banach Center Publications

1997 | 40 | 1 | 139-158
Tytuł artykułu

On Lie algebras in braided categories

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Treść / Zawartość
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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.
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EN
Czasopismo
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Tom
Numer
Strony
139-158
Opis fizyczny
Daty
wydano
1997
Twórcy
autor
• Mathematisches Institut der Universität München, Theresienstr. 39, 80333 Munich, Germany
Bibliografia
• [A] George E. Andrews, The Theory of Partitions, Encyclopedia of Mathematics and its Applications. Vol. 2, Addison-Wesley, 1976.
• [FM] Davida Fischman and Susan Montgomery, A Schur Double Centralizer Theorem for Cotriangular Hopf Algebras and Generalized Lie Algebras, J. Algebra 168 (1994), 594-614.
• [M94a] Shahn Majid, Crossed Products by Braided Groups and Bosonization, J. Algebra 163 (1994), 165-190.
• [M94b] Shahn Majid, Algebra and Hopf Algebras in Braided Categories, in: Advances in Hopf Algebras. LN pure and applied mathematics 158 (1994) 55-105.
• [R] David Radford, The Structure of Hopf Algebras with a Projection, J. Algebra 92 (1985), 322-347.
• [T] Earl J. Taft, The Order of the Antipode of Finite-dimensional Hopf algebras. Proc. Nat. Acad. Sci. USA 68 (1971), 2631-2633.
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Bibliografia
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