منابع مشابه
A Note on Divided Powers in a Hopf Algebra
The algebraic structure of a Hopf algebra over a field was established by A. Borel [l] (see Théorème 6.1). The theorem asserts that if a Hopf algebra is finitely generated in each dimension and the field is perfect then it is algebraically isomorphic to a tensor product of monogenic exterior and polynomial algebras (the latter possibly truncated if the characteristic is prime). Under more restr...
متن کاملModule Structure on Lie Powers and Natural Coalgebra-split Sub Hopf Algebras of Tensor Algebras
In this article, we investigate the functors from modules to modules that occur as the summands of tensor powers and the functors from modules to Hopf algebras that occur as natural coalgebra summands of tensor algebras. The main results provide some explicit natural coalgebra summands of tensor algebras. As a consequence, we obtain some decompositions of Lie powers over the general linear groups.
متن کاملHopf Algebras with Triality
In this paper we revisit and extend the constructions of Glauberman and Doro on groups with triality and Moufang loops to Hopf algebras. We prove that the universal enveloping algebra of any Lie algebra with triality is a Hopf algebra with triality. This allows us to give a new construction of the universal enveloping algebras of Malcev algebras. Our work relies on the approach of Grishkov and ...
متن کاملHopf Algebras with Positive Bases
We show that if a finite dimensional Hopf algebra over C has a basis such that all the structure constants are non-negative, then the Hopf algebra must be given by a finite group G and a factorization G = G+G− into two subgroups. We also show that Hopf algebras in the category of finite sets with correspondences as morphisms are classified in the similar way. Our results can be used to explain ...
متن کاملHopf Algebras with Abelian Coradical
In a previous work [AS2] we showed how to attach to a pointed Hopf algebra A with coradical kΓ, a braided strictly graded Hopf algebra R in the category Γ Γ YD of Yetter-Drinfeld modules over Γ. In this paper, we consider a further invariant of A, namely the subalgebra R of R generated by the space V of primitive elements. Algebras of this kind are known since the pioneering work of Nichols. It...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1971
ISSN: 0021-8693
DOI: 10.1016/0021-8693(71)90126-8