| Title |
Tensor subalgebras and First Fundamental Theorems in invariant theory |
| Date |
2008 |
| Summary |
Let V be an n-dimensional complex inner product space and let T := T(V) circle times 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 U(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, C) (in the sense of Weyl), the characterization has as direct consequences First Fundamental Theorems for several subgroups of GL(n, C). Moreover, a Galois correspondence between linear algebraic *-subgroups of GL(n, C) and nondegenerate contraction-closed graded *-subalgebras of T is derived. We also consider some combinatorial applications, viz. to self-dual codes and to combinatorial parameters. |
| Type |
article |
| Persistent IdentifierThe Persistent Identifiers (PI) is a number assigned to a digital object (for example a publication or dataset). By using the stable Uniform Resource Name (URN), objects will no longer be identified by the unstable Uniform Resource Locator (URL). The advantage is clear: when an object shifts to another repository, its URL will change, but its URN will remain the same. |
urn:nbn:nl:ui:29-288997 |
| Publication |
http://dare.uva.nl/record/288997 |
| Metadata |
XML |
| Export |
 (download Zotero) |
| Repository |
University of Amsterdam |
| Published in |
Journal of Algebra, Vol. 319, No. 3, p.1305-1319. |
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Tensor subalgebras and First Fundamental Theorems in invariant theory
