5 papers
Non-associative Solomon's descent algebras
J. M. Pérez-Izquierdo
Motivated by the observation that universal enveloping algebras of relatively free Sabinin algebras admit natural associative internal products, we revisit the classical relationsh…
Hyporeductive and Pseudoreductive Hopf algebras
J. M. Pérez-Izquierdo
In his generalization of reductive homogeneous spaces, Lev Sabinin showed that Lie's fundamental theorems hold for local analytic hyporeductive and pseudoreductive loops. We derive…
Linear representations of formal loops
S. Madariaga, José M. Pérez-Izquierdo
A representation of an object in a category is an abelian group in the corresponding comma category. In this paper we derive the formulas describing linear representations of objec…
Hopf algebras with triality
Georgia Benkart, Sara Madariaga, José M. Pérez-Izquierdo
In this paper we revisit and extend the constructions of Glauberman and Doro on groups with triality and Moufang loops to Hopf algebras. We prove that the universal enveloping alge…
A quantum octonion algebra
Georgia Benkart, José M. Pérez-Izquierdo
Using the natural irreducible 8-dimensional representation and the two spin representations of the quantum group (D) of D, we construct a quantum analogue of the split…