Algebras, hyperalgebras, nonassociative bialgebras and loops
Sabinin algebras are a broad generalization of Lie algebras
that include Lie, Malcev and Bol algebras as very particular examples.
We present a construction of a universal enveloping algebra for Sabinin
algebras, and the corresponding Poincaré-Birkhoff-Witt Theorem. A
nonassociative counterpart of Hopf algebras is also introduced. Loop
algebras and universal enveloping algebras of Sabinin algebras are
natural examples of these nonassociative Hopf algebras. Identities of
loops move to identities of nonassociative Hopf algebras by a
linearizing process.
(This paper will appear in Adv. Math. 208 (2007), 834-876)
J. M. Pérez-Izquierdo < j.m@dmc.unirioja.es >