Hopf algebra of projection functions

Hopf Algebra of Projection Functions

We study Hopf algebras over projection functions of the complex vector C appropriate for computing inversion formulas from discrete mathematics. Using calculus of projection functions introduced in this way, we derived various inversion formulas, including Gould’s inversion formula and its generalizations.

Gorenstein global dimensions for Hopf algebra actions

Let $H$ be a Hopf algebra and $A$ an $H$-bimodule algebra‎. ‎In this paper‎, ‎we investigate Gorenstein global dimensions for Hopf‎ ‎algebras and twisted smash product algebras $Astar H$‎. ‎Results from‎ ‎the literature are generalized‎. 

The primitives of the Hopf algebra of noncommutative symmetric functions

Let NSymm be the Hopf algebra of noncommutative symmetric functions over the integers. In this paper a description is given of its Lie algebra of primitives over the integers, Prim(NSymm), in terms of recursion formulas. For each of the primitives of a basis of Prim(NSymm), indexed by Lyndon words, there is a recursively given divided power series over it. This gives another proof of the theore...

Hopf Algebra Extensions of Monogenic Hopf Algebras

William M. Singer has described a cohomology theory of connected Hopf algebras which classifies extensions of a cocommutative Hopf algebra by a commutative Hopf algebra in much the same way as the cohomology of groups classifies extensions of a group by an abelian group. We compute these cohomology groups for monogenic Hopf algebras, construct an action of the base ring on the cohomology groups...

Hopf Algebra of Permutations