The Exponential Map for Hopf Algebras

On the Coderivations of Some Hopf Algebras

The Exponential map on the Cayley-Dickson algebras

We study the Exponential map for An = R 2 , the Cayley-Dickson algebras for n ≥ 1, which generalize the complex exponential map to Quaternions, Octonions and so forth. As an application, we show that the selfmap of the unit sphere in An, S(An) = S 2n−1, given by taking k-powers has topological degree k for k an integer number, from this we derive a suitable “Fundamental Theorem of Algebra for An.”

Hopf algebras for ternary algebras and groups

We construct an universal enveloping algebra associated to the ternary extension of Lie (super)algebras called Lie algebra of order three. A Poincaré-Birkhoff-Witt theorem is proven is this context. It this then shown that this universal enveloping algebra can be endowed with a structure of Hopf algebra. The study of the dual of the universal enveloping algebra enables to define the parameters ...

Baxter Algebras and Hopf Algebras

George E. Andrews Department of Mathematics Pennsylvania State University University Park, PA 16802, USA ([email protected]) Li Guo Department of Mathematics and Computer Science Rutgers University at Newark Newark, NJ 07102, USA ([email protected]) William Keigher Department of Mathematics and Computer Science Rutgers University at Newark Newark, NJ 07102, USA ([email protected]...

Inverting the Hopf map

We calculate the η-localization of the motivic stable homotopy ring over C, confirming a conjecture of Guillou and Isaksen. Our approach is via the motivic Adams-Novikov spectral sequence. In fact, work of Hu, Kriz and Ormsby implies that it suffices to compute the α1localization of the classical Adams-Novikov E2-term, and this is what we do. Guillou and Isaksen also propose a pattern of differ...