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- W2045493022 abstract "Given two complete atomistic lattices $${mathcal{L}}_{1}$$ and $${mathcal{L}}_{2}$$ , we define a set $${rm S}({mathcal{L}}_{1}, {mathcal{L}}_{2})$$ of complete atomistic lattices by means of three axioms (natural regarding the description of separated quantum compound systems), or in terms of a universal property with respect to a given class of bimorphisms. We call the elements of $${rm S}({mathcal{L}}_{1}, {mathcal{L}}_{2})$$ weak tensor products of $${mathcal{L}}_{1}$$ and $${mathcal{L}}_{2}$$ . We prove that $${rm S}({mathcal{L}}_{1}, {mathcal{L}}_{2})$$ is a complete lattice. We compare the bottom element $${mathcal{L}}_{1} $$ $$ {mathcal{L}}_{2}$$ with the separated product of Aerts and with the box product of Grätzer and Wehrung. Similarly, we compare the top element $${mathcal{L}}_{1} $$ $$ {mathcal{L}}_{2}$$ with the tensor products of Fraser, Chu and Shmuely. With some additional hypotheses on $${mathcal{L}}_{1}$$ and $${mathcal{L}}_{2}$$ (true for instance if $${mathcal{L}}_{1}$$ and $${mathcal{L}}_{2}$$ are moreover irreducible, orthocomplemented and with the covering property), we characterize the automorphisms of weak tensor products in terms of those of $${mathcal{L}}_{1}$$ and $${mathcal{L}}_{2}$$ ." @default.
- W2045493022 created "2016-06-24" @default.
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- W2045493022 date "2007-09-18" @default.
- W2045493022 modified "2023-10-14" @default.
- W2045493022 title "Weak tensor products of complete atomistic lattices" @default.
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- W2045493022 doi "https://doi.org/10.1007/s00012-007-2040-2" @default.
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