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Hereditary automorphic Lie algebras

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journal contribution
posted on 22.01.2020, 14:46 by Vincent KnibbelerVincent Knibbeler, Sara LombardoSara Lombardo, Jan A. Sanders
© 2019 World Scientific Publishing Company. We show that automorphic Lie algebras which contain a Cartan subalgebra with a constant-spectrum, called hereditary, are completely described by 2-cocycles on a classical root system taking only two different values. This observation suggests a novel approach to their classification. By determining the values of the cocycles on opposite roots, we obtain the Killing form and the abelianization of the automorphic Lie algebra. The results are obtained by studying equivariant vectors on the projective line. As a byproduct, we describe a method to reduce the computation of the infinite-dimensional space of said equivariant vectors to a finite-dimensional linear computation and the determination of the ring of automorphic functions on the projective line.

Funding

EPSRC (EP/E044646/1 and EP/E044646/2)

NWO VENI (016.073.026)

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Communications in Contemporary Mathematics

Volume

22

Issue

8

Pages

1950076

Publisher

World Scientific

Version

AM (Accepted Manuscript)

Publisher statement

Electronic version of an article published as Communications in Contemporary Mathematics, Volume, Issue, 2019, Pages] https://doi.org/10.1142/S0219199719500767 © [copyright World Scientific Publishing Company] https://www.worldscientific.com/worldscinet/ccm

Acceptance date

17/08/2019

Publication date

2019-12-20

Notes

29 pages

ISSN

0219-1997

eISSN

1793-6683

Language

en

Depositor

Prof Sara Lombardo Deposit date: 19 January 2020

Article number

1950076