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INVARIANTS OF LIE ALGEBRAS EXTENDED OVER COMMUTATIVE ALGEBRAS WITHOUT UNIT

    https://doi.org/10.1142/S1402925110000817Cited by:6 (Source: Crossref)

    We establish results about the second cohomology with coefficients in the trivial module, symmetric invariant bilinear forms, and derivations of a Lie algebra extended over a commutative associative algebra without unit. These results provide a simple unified approach to a number of questions treated earlier in completely separated ways: periodization of semisimple Lie algebras (Anna Larsson), derivation algebras, with prescribed semisimple part, of nilpotent Lie algebras (Benoist), and presentations of affine Kac–Moody algebras.

    AMSC: 17B20, 17B40, 17B55, 17B56, 17B67