Laguerre polynomials of derivations

Avitabile, Marina and Mattarei, Sandro (2015) Laguerre polynomials of derivations. Israel Journal of Mathematics, 205 (1). pp. 109-126. ISSN 0021-2172

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Laguerre polynomials of derivations
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Abstract

We introduce 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. We take inspiration from 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. Our grading switching is achieved by evaluating certain generalized Laguerre polynomials of degree p − 1, which play the role of generalized exponentials, on a derivation of the algebra. A crucial part of our argument is establishing a congruence for them which is an appropriate analogue of the functional equation exp(x) · exp(y) = exp(x+y) for the classical exponential. Besides having a wider scope, our treatment provides a more transparent explanation of some aspects of the original toral switching, which can be recovered as a special case.

Keywords:Lie algebras, toral switching, Laguerre polynomial, exponential, derivation, JCNotOpen
Subjects:G Mathematical and Computer Sciences > G110 Pure Mathematics
Divisions:College of Science > School of Mathematics and Physics
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ID Code:18499
Deposited On:11 Dec 2015 09:45

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