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On the classification of subalgebras of $$\text{Cend}_N$$ and $$\text{gc}_N$$. (English) Zbl 1034.17018
The authors classify all infinite subalgebras of the conformal algebras $$\text{Cend}_{N}$$ and $$\text{gc}_{N}$$ over the field $$\mathbb C$$ (these algebras are direct ‘conformal’ analogues of the matrix algebras $$M_N(\mathbb C)$$ and $$\text{gl}_N (\mathbb C)$$, respectively). For the definition of conformal algebra, see 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 $$\text{Cend}_{N}$$ .

##### MSC:
 17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) 17B68 Virasoro and related algebras 17B81 Applications of Lie (super)algebras to physics, etc. 81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, $$W$$-algebras and other current algebras and their representations
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