The second cohomology group for Kac-Moody Lie algebras and kähler differentials
نویسندگان
چکیده
منابع مشابه
Laplacian spectrum for the nilpotent Kac-Moody Lie algebras
We prove that the maximal nilpotent subalgebra of a Kac-Moody Lie algebra has a (essentially, unique) Euclidean metric with respect to which the Laplace operator in the chain complex is scalar on each component of a given degree. Moreover, both the Lie algebra structure and the metric are uniquely determined by this property.
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A Borel-Tits theory was developped for almost split forms of symmetrizable Kac-Moody Lie algebras [J. of Algebra 171, 43-96 (1995)]. In this paper, we look to almost split real forms for symmetrizable hyperbolic KacMoody Lie algebras and we establish a complete list of these forms, in terms of their Satake-Tits index, for the strictly hyperbolic ones and for those which are obtained as (hyperbo...
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متن کاملPairing Problem of Generators in Affine Kac-Moody Lie Algebras
In this paper, we discuss the pair problem of generators in affine Kac-Moody Lie algebras. For any affine Kac-Moody algebra g(A) of X l type and arbitrary nonzero imaginary root vector x, we prove that there exists some y ∈ g(A), such that g′(A) is contained in the Lie algebra generated by x and y.
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Braided-Lie bialgebras have been introduced by Majid, as the Lie versions of Hopf algebras in braided categories. In this paper we extend previous work of Majid and of ours to show that there is a braided-Lie bialgebra associated to each inclusion of Kac–Moody bialgebras. Doing so, we obtain many new examples of infinite-dimensional braided-Lie bialgebras. We analyze further the case of untwist...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1989
ISSN: 0021-8693
DOI: 10.1016/0021-8693(89)90290-1