منابع مشابه
Vanishing Resonance and Representations of Lie Algebras
We explore a relationship between the classical representation theory of a complex, semisimple Lie algebra g and the resonance varieties R(V,K) ⊂ V ∗ attached to irreducible g-modules V and submodules K ⊂ V ∧ V . In the process, we give a precise roots-and-weights criterion insuring the vanishing of these varieties, or, equivalently, the finiteness of certain modules W(V,K) over the symmetric a...
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In this paper, we study the André-Quillen homology of simplicial commutative l-algebras, l a field, having certain vanishing properties. When l has non-zero characteristic, we obtain an algebraic version of a theorem of J.-P. Serre and Y. Umeda that characterizes such simplicial algebras having bounded homotopy groups. We further discuss how this theorem fails in the rational case and, as an ap...
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The use of homological and homotopical devices, such as Tor and AndréQuillen homology, have found substantial use in characterizing commutative algebras. The primary category setting has been differentially graded algebras and modules, but recently simplicial categories have also proved to be useful settings. In this paper, we take this point of view up a notch by extending some recent uses of ...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1959
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1959-0123919-9