Tensor subalgebras and First Fundamental Theorems in invariant theory
| dc.creator | Schrijver, Alexander | |
| dc.date | 2006-04-11 | |
| dc.date.accessioned | 2026-07-07T07:10:45Z | |
| dc.date.available | 2026-07-07T07:10:45Z | |
| dc.description | Let $V=\oC^n$ and let $T:=T(V)\otimes T(V^*)$ be the mixed tensor algebra over $V$. We characterize those subsets $A$ of $T$ for which there is a subgroup $G$ of the unitary group $\UU(n)$ such that $A=T^G$. They are precisely the nondegenerate contraction-closed graded $*$-subalgebras of $T$. While the proof makes use of the First Fundamental Theorem for $\GL(n,\oC)$ (in the sense of Weyl), the characterization has as direct consequences First Fundamental Theorems for several subgroups of $\GL(n,\oC)$. Moreover, a Galois connection between linear algebraic $*$-subgroups of $\GL(n,\oC)$ and nondegenerate contraction-closed $*$-subalgebras of $T$ is derived. | |
| dc.identifier | https://arxiv.org/abs/math/0604240 | |
| dc.identifier | http://arxiv.org/abs/math/0604240 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/111520 | |
| dc.subject | Representation Theory | |
| dc.subject | Rings and Algebras | |
| dc.subject | 15A72; 20Gxx | |
| dc.title | Tensor subalgebras and First Fundamental Theorems in invariant theory | |
| dc.type | text |