Results 241 to 250 of about 3,055 (272)

Adjoint Functors and Representation Dimensions

Acta Mathematica Sinica, English Series, 2006
Let \(\widehat{\mathcal{C}}\) denote the category of coherent functors on a category \(\mathcal{C}\). Suppose that \(\mathcal{C}\) and \(\mathcal{D}\) are additive \(k\)-categories and that \(F,G\) is pair of adjoint functors between them. The author obtains comparisons of \(\text{ gl.dim}(\widehat{\mathcal{C}}) \) with \(\text{ gl.dim}(\widehat ...
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Exterior Powers of the Adjoint Representation

Canadian Journal of Mathematics, 1997
AbstractExterior powers of the adjoint representation of a complex semisimple Lie algebra are decomposed into irreducible representations, to varying degrees of satisfaction.
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Adjoint representations of exceptional Lie algebras

Theoretical and Mathematical Physics, 1987
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Ol'shanetskij, M. A., Rogov, V.-B. K.
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LIE ALGEBRAS WITH AN ALGEBRAIC ADJOINT REPRESENTATION

Mathematics of the USSR-Sbornik, 1984
An algebra R over a field K satisfies the property P locally, if P holds for every finitely generated subalgebra of R. A famous result of A. I. Kostrikin claims that every Lie algebra G satisfying the Engel condition g(ad h)\({}^ n=0\) for any g,\(h\in G\), is locally nilpotent if char K\(=0\) or char K\(=p>n\).
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