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Some problems on universal mappings

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First we describe inductive limits for some families of Lie algebras and groups. We also consider the linear mappings from the space C(S, R) (smooth functions on a circle) to Lie algebras such that the following Local Communitatirity Property is satisfied: for only two functions with disjoint supports the corresponding elements of Lie algebra commute; we describe a universal mapping with this property.

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Pages

367-371

References

[1] W.Nahm, Quantium Field Theories in one and two dimensions, Duke mathematical Journal, 1987, v.54, No.2, pp. 579-613. [2] Serre J.P., Arbres, amalgams et SL2, 1977, Soc. Math. France, Asterisque, v. 46, 20-43. [3] C. Godbillon, Geometric differentielle et Mechanique analytique, 1969, Herman, Paris. [4] Ismagilov R.S., On a group of volume preserving diffeomorphisms, Izvestija Academii nauk SSSR, ser. math., 1980, v.44, No 4, pp. 831-867.

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