Representation theory of the Witt algebra
For the smallest nonclassical restricted Lie algebra \(L=W(1:1)\) the representation and cohomology theory is studied. Let \(\chi \) be a linear function on \(L\) and \(u(L, \chi)\) a \(\chi \)-reduced enveloping algebra, i.e. \(u(L, \chi)=U(L)/J\) where \(J\) is the ideal of \(U(L)\) generated by \(x^p-x^{[p]}-\chi (x)^p1, x\in L.\) The dimensions of the projective indecomposable \(u(L, \chi)\)-modules and mutiplicities of their composition factors are determined. The support varieties and complexities of simple \(u(L, \chi)\)-modules are computed. The orbits of the characters \(\chi \) under the action of the automorphism group are described.
scientific article; zbMATH DE number 1200007
scientific article