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8 - Infinite-dimensional Lie Algebras and Their Multivariable Generalizations

Published online by Cambridge University Press:  25 November 2023

Edited by
David Jordan ,
Nadia Mazza  and
Sibylle Schroll
David Jordan
Affiliation:
University of Edinburgh
Nadia Mazza
Affiliation:
Lancaster University
Sibylle Schroll
Affiliation:
Universität zu Köln
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Summary

The loop algebra, consisting of Laurent polynomials valued in a Lie algebra, admits a non-trivial central extension for each choice of invariant pairing on it. This affine Lie algebra and its cousin, the Virasoro algebra, are foundational objects in representation theory and conformal field theory. A natural question then arises: do there exist multivariable, or higher dimensional, generalizations of the affine algebra?

Keywords

infinite-dimensional Lie algebrasmultivariable algebras
Type
Chapter
Information
Modern Trends in Algebra and Representation Theory , pp. 273 - 316
Publisher: Cambridge University Press
Print publication year: 2023

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