Alexander Sergeev
(Balakovo Institute for Technics, Technology and
Control, and the Isaac Newton Institute)
sergeev@bittu.org.ru, sfmser01@newton.cam.ac.uk
Let V be a finite-dimensional superspace over complex numbers and g a simple matrix Lie superalgebra, i.e., a Lie subsuperalgebra of gl(V). By the classical invariant theory for g we mean the description of the g-invariants of the algebra A, where A is generated by the coordinates of (given) finite numbers of elements of V, V*, ΠV, ΠV*. (Π is the parity reversion functor.)
We give a description of the generators in the algebra of invariants and describe the relations between the invariants of scalar product type.