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math.RA2018
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…
math.RA2017
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…
math.RA2011
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…