Grading switching for modular non-associative algebras

Avitabile, Marina and Mattarei, Sandro (2015) Grading switching for modular non-associative algebras. Contemporary Mathematics . ISSN 0271-4132

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Abstract

We describe a grading switching for arbitrary non-associative 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 Artin-Hasse 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:Non-associative algebra; grading; derivation; Artin-Hasse 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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