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Conjugacy of Cartan subalgebras in EALAs with a non-fgc centreless core


Authors: V. Chernousov, E. Neher and A. Pianzola
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva, tom 78 (2017), vypusk 2.
Journal: Trans. Moscow Math. Soc. 2017, 235-256
MSC (2010): Primary 17B67; Secondary 16S36, 17B40
DOI: https://doi.org/10.1090/mosc/271
Published electronically: December 1, 2017
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Abstract: We establish the conjugacy of Cartan subalgebras for extended affine Lie algebras whose centreless core is ``of type A'', i.e., $ \ell \times \ell $-matrices over a quantum torus $ \mathcal {Q}$ whose trace lies in the commutator space of $ \mathcal {Q}$. This settles the last outstanding part of the conjugacy problem for Extended Affine Lie Algebras that remained open.


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Additional Information

V. Chernousov
Affiliation: Department of Mathematics, University of Alberta, Edmonton, Canada
Email: chernous@math.ualberta.ca

E. Neher
Affiliation: Department of Mathematics and Statistics, University of Ottawa, Ottawa, Canada
Email: neher@uottawa.ca

A. Pianzola
Affiliation: Department of Mathematics, University of Alberta, Edmonton, Canada —and— Centro de Altos Estudios en Ciencia Exactas, Buenos Aires, Argentina
Email: a.pianzola@gmail.com

DOI: https://doi.org/10.1090/mosc/271
Keywords: Extended affine Lie algebras, Lie torus, Cartan subalgebras, quantum torus, special linear Lie algebra
Published electronically: December 1, 2017
Additional Notes: V.Chernousov was partially supported by the Canada Research Chairs Program and an NSERC research grant
E.Neher was partially supported by a Discovery grant from NSERC
A.Pianzola wishes to thank NSERC and CONICET for their continuous support
The second author wishes to thank the Department of Mathematical Sciences at the University of Alberta for hospitality during part of the work on this paper
Dedicated: Dedicated to E.B.Vinberg on the occasion of his 80th birthday
Article copyright: © Copyright 2017 V.Chernousov, E.Neher, A.Pianzola

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