
We compute the cohomology of the maximal nilpotent Lie algebra of an affine Lie algebra g ^ \hat {\mathfrak {g}} with coefficients in modules of functions on the circle with values in a representation space of g \mathfrak {g} . These modules are not highest weight modules and are somewhat similar to the adjoint representation.
Solvable, nilpotent (super)algebras, Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras, affine Lie algebra, maximal nilpotent Lie algebra, cohomology, Cohomology of Lie (super)algebras
Solvable, nilpotent (super)algebras, Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras, affine Lie algebra, maximal nilpotent Lie algebra, cohomology, Cohomology of Lie (super)algebras
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