Polynomial Identities for Tangent Algebras of Monoassociative Loops
- Bremner, M.R. 2
- Madariaga, S. 1
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1
Universidad de La Rioja
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2
University of Saskatchewan
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ISSN: 0092-7872
Datum der Publikation: 2014
Ausgabe: 42
Nummer: 1
Seiten: 203-227
Art: Artikel
Andere Publikationen in: Communications in Algebra
Projekte im Zusammenhang
Zusammenfassung
We introduce degree n Sabinin algebras, which are defined by the polynomial identities up to degree n in a Sabinin algebra. Degree 4 Sabinin algebras can be characterized by the polynomial identities satisfied by the commutator, associator, and two quaternators in the free nonassociative algebra. We consider these operations in a free power associative algebra and show that one of the quaternators is redundant. The resulting algebras provide the natural structure on the tangent space at the identity element of an analytic loop for which all local loops satisfy monoassociativity, a 2 a ≡ aa 2. These algebras are the next step beyond Lie, Malcev, and Bol algebras. We also present an identity of degree 5 which is satisfied by these three operations but which is not implied by the identities of lower degree. © 2014 Copyright Taylor and Francis Group, LLC.