Homological properties of color Lie superalgebras

Details Homological properties of color Lie superalgebras Homological properties of color Lie superalgebras

2005-06-14

arxiv.org/abs/math/0506262v2

Advances in ring theory (Granville, OH, 1996), 287--293, Trends Math., Birkhauser, Boston, MA, 1997

Mathematics

Rings and Algebras

This 7-page article appeared in a conference proceedings which is now out of print

Scientific paper

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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