Dimension injective des produits croisés

• Autores: Marie-Paule Malliavin
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 46, Fasc. 1-2, 1995 (Ejemplar dedicado a: Professor Paul Dubreil (In memoriam )), págs. 121-130
• Idioma: francés
• Enlaces
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• Resumen

  • Let $k$ be a field, $R$ a commutative noetherian Gorenstein $k$-algebra of finite Krull dimension, $\mathfrak{G}$ a finite dimensional Lie algebra over $k$ which operates on $R$ by $k$-derivations and $\sigma$ a 2-cocycle of $\mathfrak{G}$ with coefficients in $R$; we will denote by $R\ast_\sigma\mathfrak{G}$ the crossed product of $R$ by mean of $\sigma$; then we will provethe inequalities: $$\mbox{injdim }R\leq \mbox{injdim } R\ast_\sigma\mathfrak{G}\leq \mbox{injdim }R + \mbox{dim } \mathfrak{G}.$$ We will give also a formula relating injdim $R\ast_\sigma\mathfrak{G}$ with the Ore localisations of this algebra with respect to the prime ideals of $R$.

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