Mathematics – Representation Theory
Scientific paper
2006-05-07
J. Algebra 317, 111-152 (2007)
Mathematics
Representation Theory
A few typos corrected, final version
Scientific paper
For any vertex algebra V and any subalgebra A of V, there is a new subalgebra of V known as the commutant of A in V. 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 (ie, a pair of mutual commutants) in the vertex algebra setting.
Lian Bong H.
Linshaw Andrew R.
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