کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4587963 1334166 2008 15 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Tensor subalgebras and first fundamental theorems in invariant theory
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Tensor subalgebras and first fundamental theorems in invariant theory
چکیده انگلیسی

Let V be an n-dimensional complex inner product space and let T:=T(V)⊗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=TG. 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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 319, Issue 3, 1 February 2008, Pages 1305-1319