Journal of the Mathematical Society of Japan

Algebraic structures on quasi-primary states in superconformal algebras


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Operator Product Expansions give algebraic structures on subspaces of quasi-primary vectors in superconformal algebras. The structures characterize the structures of superconformal algebras if they meet a criteria, while in some cases the spaces of quasi-primary vectors are finite dimensional. As an application the complete list of simple physical conformal superalgebras is given by classifying the corresponding algebraic structures on finite dimensional vector spaces. The list contains a one-parameter family of superconformal algebras with 4 supercharges that is simple for general values.

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J. Math. Soc. Japan, Volume 57, Number 2 (2005), 309-332.

First available in Project Euclid: 14 September 2006

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Zentralblatt MATH identifier

Primary: 81R05: Finite-dimensional groups and algebras motivated by physics and their representations [See also 20C35, 22E70]
Secondary: 81R10: Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, $W$-algebras and other current algebras and their representations [See also 17B65, 17B67, 22E65, 22E67, 22E70] 17B68: Virasoro and related algebras

Lie algebra Virasoro algebra Superconformal algebra Operator Product Expansion


YAMAMOTO, Go. Algebraic structures on quasi-primary states in superconformal algebras. J. Math. Soc. Japan 57 (2005), no. 2, 309--332. doi:10.2969/jmsj/1158242061.

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