ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

7. Lie Groups and Lie Algebras

1991 MS Classification: 17B65 Baranov, Alexander, Institute of Mathematics of the Academy of Sciences of Belarus, Belarus Finitary simple Lie algebras A Lie algebra is called finitary if it consists of finite-rank transformations of a vector space. Finitary simple Lie algebras over a field F of characteristic zero are classified. Below is the list of all complex (see [1]) and real finitary simple Lie algebras of countable dimension. They can be represented as the direct limits of natural embeddings of the relevant finite-dimensional algebras.

F = C: sl_{∞}(C), so_{∞}(C), sp_{∞}(C). F = R: sl_{∞}(C), so_{∞}(C), sp_{∞}(C); sl_{∞}(R), su_{∞}(C, k), sl_{∞}(H), so_{∞}(R, k), so_{∞}(H, k), sp_{∞}(R), sp_{∞}(H), k = 0, 1, …, ∞.

Reference: [1] A. A. Baranov, Simple diagonal locally finite Lie algebras, Proc. London Math. Soc. (to appear).