Rationality of Hilbert series in noncommutative invariant theory

A Hilbert-nagata Theorem in Noncommutative Invariant Theory

Nagata gave a fundamental sufficient condition on group actions on finitely generated commutative algebras for finite generation of the subalgebra of invariants. In this paper we consider groups acting on noncommutative algebras over a field of characteristic zero. We characterize all the T-ideals of the free associative algebra such that the algebra of invariants in the corresponding relativel...

Hilbert Series and Degree Bounds in Invariant Theory

The Hilbert series and degree bounds play signiicant roles in computational invariant theory. In the modular case, neither of these tools is available in general. In this article three results are obtained, which provide partial remedies for these shortcomings. First, it is shown that the so-called extended Hilbert series, which can always be calculated by a Molien type formula, yields strong c...

The Rationality Problem in Invariant Theory

ii Contents Introduction v 1 The rationality problem in invariant theory 1 1. iii iv CONTENTS Introduction Invariant theory as a mathematical discipline on its own originated in Eng-land around the middle of the nineteenth century with Cayley's papers on hyperdeterminants and his famous Memoirs on Quantics, followed by Salmon, Sylvester and Boole, and Aronhold, Clebsch and Gordan in Germany. Th...

Noncommutative Extensions of Hilbert Rings

Lorentz invariant and supersymmetric interpretation of noncommutative quantum field theory

In this paper, based on recent work [13] 1 , we construct deformed Poincaré SUSY algebra in terms of twisted (Hopf) algebra. By adapting this new interpretation of superPoincaré algrebra as our fundamental symmetry, we can construct Lorentz and Poincaré SUSY invariant quantum field theory on the non(anti)commutative (super)space. The key point is validity of our new twist element that guarantee...