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Howe pairs in the theory of vertex algebras
- Source :
-
Journal of Algebra . Nov2007, Vol. 317 Issue 1, p111-152. 42p. - Publication Year :
- 2007
-
Abstract
- Abstract: For any vertex algebra and any subalgebra , there is a new subalgebra of known as the commutant of in . This construction was introduced by Frenkel–Zhu, and is a generalization of an earlier construction due to Kac–Peterson and Goddard–Kent–Olive known as the coset construction. In this paper, we interpret the commutant as a vertex algebra notion of invariant theory. We present an approach to describing commutant algebras in an appropriate category of vertex algebras by reducing the problem to a question in commutative algebra. We give an interesting example of a Howe pair (i.e., a pair of mutual commutants) in the vertex algebra setting. [Copyright &y& Elsevier]
- Subjects :
- *MATHEMATICS
*ALGEBRA
*MATHEMATICAL analysis
*LINEAR algebra
Subjects
Details
- Language :
- English
- ISSN :
- 00218693
- Volume :
- 317
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 26678273
- Full Text :
- https://doi.org/10.1016/j.jalgebra.2007.07.002