Invariant forms of the elementary unitary Lie superalgebra. (Q1408353)

Let \(K\) be a unital associative superring containing \(\frac{1}{2}\) and \(L = L_{\overline 0} \oplus L_{\overline 1}\) a Lie superalgebra over \(K\). For \(L\) having a grading \(\bigoplus_{\sigma \in K} L_\sigma\) determined by the diagonal action on \(L\) of a toral element \(h_0 \in L_0 \cap L_{\overline 0}\) and certain other conditions on \(L_0\) and \(\{ \sigma \in K \mid L_\sigma \not= 0\}\); the author describes the supersymmetric invariant forms of \(L\) in terms of \(K\)-linear maps from \(L_0\) to \(K\) satisfying certain conditions. She also specifically studies the invariant forms of the elementary unitary Lie superalgebra; which is defined on certain endomorphisms of an \(\mathfrak a\)-supermodule with a \(\rho\)-Hermitian form \(\chi\) (for \(\rho = \pm 1\)); where \(\mathfrak a\) is a unital associative superalgebra over \(K\) with a superinvolution.