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Homological properties of color Lie superalgebras

Kenneth L. Price
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Abstract

Let $\mathcal{L}=\mathcal{L}_{+}\oplus \mathcal{L}_{-}$ be a finite dimensional color Lie superalgebra over a field of characteristic 0 with universal enveloping algebra $U(\mathcal{L})$. We show that $\limfunc{gldim}(U(\mathcal{L}_{+}))= \limfunc{lFPD}(U(\mathcal{L}))= \limfunc{rFPD}(U(\mathcal{L}))= \limfunc{injdim}_{U(\mathcal{L})}(U(\mathcal{L}))= \dim (\mathcal{L}_{+})$. We also prove that $U(\mathcal{L})$ is Auslander-Gorenstein and Cohen-Macaulay and thus that it has a QF classical quotient ring.

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Kenneth L. Price. 2005-06-14. Homological properties of color Lie superalgebras. https://arxiv.org/abs/math/0506262

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