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d-Representability of simplicial complexes of fixed dimension
Combinatorics d-Representability fixed dimension
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2011/8/26
Abstract: Let K be a simplicial complex with vertex set V = {v_1,..., v_n}. The complex K is d-representable if there is a collection {C_1,...,C_n} of convex sets in R^d such that a subcollection {C_{...
Brown representability often fails for homotopy categories of complexes
Brown representability Adjoint functor Triangulated cate-gory
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2011/2/22
We show that for the homotopy category K(Ab) of com-plexes of abelian groups, both Brown representability and Brown repre-sentability for the dual fail. We also provide an example of a localizing subc...
Representability of derived stacks
Representability of derived stacks math
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2010/11/15
Lurie's representability theorem gives necessary and sufficient conditions for a functor to be an almost finitely presented derived geometric stack. We establish several variants of Lurie's theorem, ...
Quantum codes give counterexamples to the unique pre-image conjecture of the N-representability problem
Quantum codes give counterexamples the unique pre-image conjecture N-representability problem
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2010/11/5
It is well known that the ground state energy of many-particle Hamiltonians involving only 2-body interactions can be obtained using constrained optimizations over density matrices which arise from r...
Some Applications of the Lattice Finite Representability in Spaces of Measurable Functions
Integral operators Ultraproducts of spaces and maps
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2010/3/1
We study the lattice finite representability of the Bochner space Lp(m1,Lq(m2)) in \ellp{\ellq}, 1 \le p,q < \infty, and then we characterize the ideal of the operators which factor through a lattice ...
Failure of Brown representability in derived categories
Brown representability derived categories
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2010/10/29
Let T be a triangulated category with coproducts, C the full subcategory of compact objects in T. If T is the homotopy category of spectra, Adams proved the following in [Adams71]: All contravariant ...