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Semidefinite functions on categories
, 2009
"... Freedman, Lovász and Schrijver characterized graph parameters that can be represented as the (weighted) number of homomorphisms into a fixed graph. Several extensions of this result have been proved. We use the framework of categories to prove a general theorem of this kind. Similarly as previous re ..."
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Freedman, Lovász and Schrijver characterized graph parameters that can be represented as the (weighted) number of homomorphisms into a fixed graph. Several extensions of this result have been proved. We use the framework of categories to prove a general theorem of this kind. Similarly as previous results, the characterization uses certain infinite matrices, called connection matrices, which are required to be positive semidefinite.
Tensor subalgebras and First Fundamental Theorems in invariant theory
 JOURNALOF THE AMERICAN MATHEMATICAL SOCIETY. ARXIV:MATH.CO/0505035
, 2006
"... Let V = C n 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 = T G. They are precisely the nondegenerate contractionclosed graded ∗subalgebras of T. While the proof makes us ..."
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Cited by 2 (1 self)
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Let V = C n 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 = T G. They are precisely the nondegenerate contractionclosed 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 connection between linear algebraic ∗subgroups of GL(n, C) and nondegenerate contractionclosed ∗subalgebras of T is derived.