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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, Università di Milano-Bicocca, via Cozzi 53, 20125 Milano, Italy marina.avitabile@unimib.it Sandro Mattarei Dipartimento di Matematica, Università degli Studi di Trento, via Sommarive 14, 38050 Povo (Trento), Italy mattarei@science.unitn.it 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 [ Fulltext-pdf (287 KB)] for subscribers only. |