In this paper, we establish a structure theorem for connected graded Hopf algebras over a field of characteristic 0 by claiming the existence of a family of homogeneous generators and a total order on the index set that satisfy some desirable conditions. The approach to the structure theorem is...
We construct spectral sequences which provide a way to compute the cohomology theory that classifies extensions of graded connected Hopf algebras over a commutative ring as described by William M. Singer. Specifically, for ( A , B ) an a... GD Henderson - 《Journal of Algebra》 被引量: 0...
Thus, both Ar and A are graded polynomial algebras over their spaces of primitives, Pr=⊕mPmr and P=⊕mPm. Framed knots differ from knots only by a single integer parameter (the “self-linking,” itself a type 1 invariant). Thus, Pr and P are also closely related. Theorem 7 (Bar-...
Let H be a finite-dimensional connected Hopf algebra over an algebraically closed field k of characteristic p>0p>0. We provide the algebra structure of the associated graded Hopf algebra gr H. Then, we study the case when H is generated by a Hopf subalgebra K and another element and the...
Connected (graded) Hopf algebrasdoi:10.1090/TRAN/7686Ken BrownPaul GilmartinJames J. ZhangAmerican Mathematical Society (AMS)
We show that if A is a graded connected Hopf algebra over a field of characteristic 0, such that all homogeneous elements of strictly positive degree are nilpotent, then A is commutative and cocommutative. Hence A is an exterior algebra over the primitive elements....
Hopf algebrasLie algebrasConnectedCoradically gradedCocommutativeAbstract Let H be a finite-dimensional connected Hopf algebra over an algebraically closed field k of characteristic p > 0 . We provide the algebra structure of the associated graded Hopf algebra gr聽H. Then, we study the case when ...
Connected graded Hopf algebraAdams operatorHopf powerSweedler powerPBW basisLyndon wordThe Adams operators on a Hopf algebraHare the convolution powers of the identity map ofH. They are also called Hopf powers or Sweedler powers. It is a natural family of operators onHthat contains the antipode....
0.~ TROIXCTIOS suppose is a diagram of graded connected Hopf algebras over a fixed ground ring K. We call (0.1) an extension of B by A if C is isomorphic to A@ I? simultancously as a left A-module and right B-comodule. Both the algehra and coa! gebra...
Hopf algebrasLie algebrasConnectedCoradically gradedCocommutativeLet H be a finite-dimensional connected Hopf algebra over an algebraically closed field k of characteristic p>0. We provide the algebra structure of the associated graded Hopf algebra grH. Then, we study the case when H is generated ...