 About 5,430 results  books.google.com I Let H be a Hopf algebra and G(H) the group of grouplike elements of H. If g, h
G G(H), then an element x € H is called (g, /i)primitive if A(x) — x ® g + h® x. The
set of all (g, /i)primitive elements of H is denoted by Pg^(H). A (1, l)primitive is ... 

 books.google.com Stefaan Caenepeel, A Verschoren  1998  Preview The biproduct kC3 *k[x]/(x3) is isomorphic to the Hopf algebra if we associate r#l
and t resp. )#x and x. 2 SKEW PRIMITIVE ELEMENTS The last example shows
the importance of elements x e H (a Hopf algebra in with A(x) — x ® I + 1 ® x. 

 books.google.com Jeffrey Bergen, Stefan Catoiu, William Chin  2004  Preview If M = TV then Kp(N,£) is isomorphic to the Taft algebra. Proposition 12. Le* H be
a nonsemisimple finite dimensional Hopf algebra overk. Suppose that there
exists a nontrivial skewprimitive element. Then H contains a Hopf subalgebra K
... 

 books.google.com Recall that an element X in a Hopf algebra H. is said to be grouplike if A(X) =X®
X and is said to be primitive if A(X) = X ®1 + 1®X. If G denotes the affine group
scheme of a commutative Hopf algebra H, then a grouplike element X G 7i ... 

 books.google.com Nicolás Andruskiewitsch, Juan Cuadra, Blas Torrecillas  2013  Preview By Proposition 4.12(iv), it remains only to show that H, H∗ have pointed subHopf
algebras of dimension 8. Let K = 〈G(H),x〉, the subHopf algebra of H generated
by G(H) and a nontrivial skewprimitive element. Then dimK < 8p and is divisible
... 

 books.google.com ... (rij) denotes the canonical set of generators of 0,(GL(n))). Recall that the set of
grouplike elements of a Hopf algebra H is denoted by G(H). Given g, h e G(H),
the set of (g, h)skew primitive elements is P„h (H) := {u E H  A(u) = g & u + u & h}. 

 books.google.com Note that when G is finite we have already attached another Hopf algebra C(G) to
G. These two Hopf algebras are dual to each other in a sense to be ... A primitive
element of a Hopf algebra is an element h e H such that A/i = 1 <8>/i + h ® 1. 

 books.google.com A quick calculation shows that the Rmodule PA of primitive elements of a Hopf
algebra A is a Lie subalgebra. The universal property of U(PA) thus gives a
natural map of Hopf algebras g : U(PA) → A, and g is clearly an epimorphism if A
is ... 

 books.google.com Let /\(x\, . . . i^n) be the exterior algebra generated by the elements x\, . . . , xn of
odd degree. We can define a Hopf algebra structure imposing that the elements
xt are primitive elements. The dual of this Hopf algebra is again the exterior ... 

 books.google.com Using the dendriform and bidendriform CartierQuillenMilnorMoore theorem, we
construct a basis of the space of primitive elements of the Hopf algebra of free
quasisymmetric functions, indexed by a certain set of trees, and inductively ... 

 