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Zbl 1034.17018
Boyallian, Carina; Kac, Victor G.; Liberati, Jose I.
On the classification of subalgebras of $\text{Cend}_N$ and $\text{gc}_N$. (English)
[J] J. Algebra 260, No. 1, 32-63 (2003). ISSN 0021-8693

The authors classify all infinite subalgebras of the conformal algebras $\text{Cend}_{N}$ and $\text{gc}_{N}$ over the field $\Bbb C$ (these algebras are direct `conformal' analogues of the matrix algebras $M_N(\Bbb C)$ and $\text{gl}_N (\Bbb C)$, respectively). For the definition of conformal algebra, see {\it V. G. Kac}, Vertex algebras for beginners. 2nd ed. University Lecture Series. 10. Providence, RI: American Mathematical Society (AMS) (1998; Zbl 0924.17023). They describe all finite irreducible modules over $\text{Cend}_{N,P}$. The authors also describe all automorphisms of $\text{Cend}_{N,P}$ and classify all homomorphisms and anti-homomorphisms of $\text{Cend}_{N,P}$ to $\text{Cend}_{N}$ .
[Yong-Qing Chen (Shenzhen)]

MSC 2000:: *17B99 Lie algebras
81R10 Repres. of infinite-dim. groups and algebras from quantum theory
16S99 Associative rings and algebras arising under various constructions

Keywords: conformal algebras; classification; automorphisms; analogue of Burnside theorem

Citations: Zbl 0924.17023

Cited in: Zbl 1166.17303

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