A central question in invariant theory is that of determining the relations among invariants. Geometric invariant theory quotients come with a natural ample line bundle, and hence often a natural projective embedding. This question translates to determining the equations of the moduli space under this embedding. This article deals with one of the most classical quotients, the space of ordered p...

Abstract The problem of finding generators the subalgebra invariants under action a group automorphisms finite-dimensional Lie algebra on its universal enveloping is reduced to homogeneous same acting symmetric tensor algebra. This process applied prove constructive Hilbert–Nagata Theorem (including degree bounds) for in nilpotent relatively free associative endowed with an induced by represent...

Using arguments based on BRST cohomology, the pure spinor formalism for the su-perstring in an AdS 5 × S 5 background is proven to be BRST invariant and conformally invariant at the quantum level to all orders in perturbation theory. Cohomology arguments are also used to prove the existence of an infinite set of non-local BRST-invariant charges at the quantum level.

Using arguments based on BRST cohomology, the pure spinor formalism for the su-perstring in an AdS 5 × S 5 background is proven to be BRST invariant and conformally invariant at the quantum level to all orders in perturbation theory. Cohomology arguments are also used to prove the existence of an infinite set of non-local BRST-invariant charges at the quantum level.