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The category of Yetter-Drinfeld modules YD K K over a Hopf algebra K (with bijektive antipode over a field k) is a braided monoidal category. If H is a Hopf algebra in this category then the primitive elements of H do not form an ordinary Lie algebra anymore. We introduce the notion of a (generalized) Lie algebra in YD K K such that the set of primitive(More)
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.(More)
The theory of Hopf algebras is closely connected with various applications , in particular to algebraic and formal groups. Although the rst occurence of Hopf algebras was in algebraic topology, they are now found in areas as remote as combinatorics and analysis. Their structure has been studied in great detail and many of their properties are well(More)
A ring primitive on the right but not on the left, 473, 1000. Berkson, A. J. The u-algebra of a restricted Lie algebra is Frobenius, 14. Bialynicki-Birula, A. On the inverse Problem of Galois theory of differential fields, 960. Bojanic, R. and Musielak, J. An inequality for functions with derivatives in an Orlicz Space, 902. Bouwsma, W. D. Zeros of(More)
– 1950's The main applications were originally in the fields of algebraic topology, particularly homology theory, and abstract algebra. – 1960's Grothendieck et al. began using category theory with great success in algebraic geometry. – 1970's Lawvere and others began applying categories to logic, revealing some deep and surprising connections. – 1980's(More)