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Journal of Lie Theory 24 (2014), No. 2, 457--473
Copyright Heldermann Verlag 2014

Nottingham Lie Algebras with Diamonds of Finite and Infinite Type

Marina Avitabile
Dipartimento di Matematica e Applicazioni, UniversitÓ di Milano-Bicocca, via Cozzi 53, 20125 Milano, Italy

Sandro Mattarei
Dipartimento di Matematica, UniversitÓ degli Studi di Trento, via Sommarive 14, 38050 Povo (Trento), Italy

We consider a class of infinite-dimensional, modular, graded Lie algebras, which includes the graded Lie algebra associated to the Nottingham group with respect to its lower central series. We identify two subclasses of Nottingham Lie algebras as loop algebras of finite-dimensional simple Lie algebras of Hamiltonian Cartan type. A property of Laguerre polynomials of derivations, which is related to toral switching, plays a crucial role in our constructions.

Keywords: Modular Lie algebra, graded Lie algebra, thin Lie algebra.

MSC: 17B50; 17B70, 17B65, 17B56

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