Avitabile, Marina and Mattarei, Sandro (2015) Grading switching for modular nonassociative algebras. Contemporary Mathematics . ISSN 02714132
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Item Type:  Article 

Item Status:  Live Archive 
Abstract
We describe a grading switching for arbitrary nonassociative algebras of prime characteristic p, aimed at producing a new grading of an algebra from a given one. This is inspired by a fundamental tool in the classification theory of modular Lie algebras known as toral switching, which relies on a delicate adaptation of the exponential of a derivation.
We trace the development of grading switching, from an early version based on taking the ArtinHasse exponential of a nilpotent derivation, to a more general version which uses certain generalized Laguerre polynomials playing the role of generalized exponentials. Both versions depend on the existence of appropriate analogues of the functional equation exp(x).exp(y=exp(x+y) for the classical exponential.
Keywords:  Nonassociative algebra; grading; derivation; ArtinHasse exponential; Laguerre polynomial; restricted Lie algebra; toral switching, bmjtype, NotOAChecked 

Subjects:  G Mathematical and Computer Sciences > G110 Pure Mathematics 
Divisions:  College of Science 
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ID Code:  24988 
Deposited On:  16 Nov 2016 20:48 
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