Associative conformal algebras of linear growth. (English) Zbl 1151.17312
Kac introduced the notion of (Lie) conformal algebra as the local structure of a certain Lie algebra with one-variable structure. The conformal algebra is equivalent to the structure of positive modes of a vertex algebra. The author classifies finitely generated simple unital associative conformal algebras of linear growth. An associative conformal algebra is equivalent to what I called “Gelfand-Dorfman operator algebra” in my paper [Lett. Math. Phys. 33, No. 1, 1–6 (1995; Zbl 0837.16034)] where I proved that such an algebra is equivalent to an associative algebra with a derivation under a certain unital condition.
Reviewer: Xu Xiaoping (Kowloon)
MSC:
| 17B69 | Vertex operators; vertex operator algebras and related structures |
| 16P90 | Growth rate, Gelfand-Kirillov dimension |
| 16S32 | Rings of differential operators (associative algebraic aspects) |
Keywords:
conformal identity; unital associative conformal algebras; conformal algebras of linear growth; Gelfand-Kirillov dimensionCitations:
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