In the paper one- and two-dimensional cohomology is compared for finite and infinite nilpotent Lie algebras, with coefficients in the adjoint representation. It turns out that, because the adjoint representation is not a highest weight representation in infinite dimension, the considered cohomology
โฆ LIBER โฆ
Differentiation of some infinite-dimensional topologically nilpotent Lee algebras
โ Scribed by Yu. B. Khakimdzhanov
- Publisher
- SP MAIK Nauka/Interperiodica
- Year
- 1990
- Tongue
- English
- Weight
- 343 KB
- Volume
- 48
- Category
- Article
- ISSN
- 0001-4346
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Given a nontrivial torsion-free abelian group (A, +, 0), a field F of characteristic 0, and a nondegenerate bi-additive skew-symmetric map cp : A x A -+ F, we study the Lie algebra \_Y(A, cp) over F with basis {ex: x E A\(O)} an multiplication [ex,ey] = cp(x, y)e,+,. We show that d Y(A, 'p) is simpl