Homological properties of color Lie superalgebras
Abstract
Description
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.
This 7-page article appeared in a conference proceedings which is now out of print
This 7-page article appeared in a conference proceedings which is now out of print