منابع مشابه
On the Structure of Cofree Hopf Algebras
We prove an analogue of the Poincaré-Birkhoff-Witt theorem and of the Cartier-Milnor-Moore theorem for non-cocommutative Hopf algebras. The primitive part of a cofree Hopf algebra is a B∞-algebra. We construct a universal enveloping functor U2 from B∞-algebras to 2-associative algebras, i.e. algebras equipped with two associative operations. We show that any cofree Hopf algebra H is of the form...
متن کاملThe Hopf Algebras of Non-commutative Symmetric Functions and Quasisymmetric Function Are Free and Cofree
We uncover the structure of the space of symmetric functions in non-commutative variables by showing that the underlined Hopf algebra is both free and co-free. We also introduce the Hopf algebra of quasi-symmetric functions in non-commutative variables and define the product and coproduct on the monomial basis of this space and show that this Hopf algebra is free and cofree. In the process of l...
متن کاملThe Hopf Algebras of Symmetric Functions and Quasisymmetric Functions in Non-commutative Variables Are Free and Cofree
We uncover the structure of the space of symmetric functions in non-commutative variables by showing that the underlined Hopf algebra is both free and co-free. We also introduce the Hopf algebra of quasi-symmetric functions in non-commutative variables and define the product and coproduct on the monomial basis of this space and show that this Hopf algebra is free and cofree. In the process of l...
متن کاملThe Hopf Algebra of Non-commutative Symmetric Functions and Quasi-symmetric Functions Are Free and Cofree
We uncover the structure of the space of symmetric functions in non-commutative variables by showing that the underlined Hopf algebra is both free and co-free. We also introduce the Hopf algebra of quasi-symmetric functions in non-commutative variables and define the product and coproduct on the monomial basis of this space and show that this Hopf algebra is free and cofree. In the process of l...
متن کاملFinitely Generated Invariants of Hopf Algebras on Free Associative Algebras
We show that the invariants of a free associative algebra of finite rank under a linear action of a finite-dimensional Hopf algebra generated by group-like and skew-primitive elements form a finitely generated algebra exactly when the action is scalar. This generalizes an analogous result for group actions by automorphisms obtained by Dicks and Formanek, and Kharchenko.
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2012
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2011.07.010