Representations of the Lie algebra of vector fields on a sphere
Journal article, 2019

For an affine algebraic variety X we study a category of modules that admit compatible actions of both the algebra A of functions on X and the Lie algebra of vector fields on X. In particular, for the case when X is the sphere S-2, we construct a set of simple modules that are finitely generated over A. In addition, we prove that the monoidal category that these modules generate is equivalent to the category of finite-dimensional rational GL(2)-modules.

Author

Yuly Billig

Carleton University

Jonathan Nilsson

Chalmers, Mathematical Sciences, Algebra and geometry

University of Gothenburg

Journal of Pure and Applied Algebra

0022-4049 (ISSN)

Vol. 223 8 3581-3593

Subject Categories

Algebra and Logic

Geometry

Mathematical Analysis

DOI

10.1016/j.jpaa.2018.11.018

More information

Latest update

8/8/2019 1