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Results tagged with lattices
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user 25998
Lattices in the sense of discrete subgroups of Euclidean spaces, as used in number theory, discrete geometry, Lie groups, etc. (Not to be confused with lattice theory or lattices as used in physics! For lattices (ordered sets), use the tag: [lattice-theory])
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Cancellation theorem for lattices
Typical examples are the hyperbolic lattices $U$ and the root lattices $A_{n}, D_{n}, E_{n}$ associated to Dynkin matrices. … In general we cannot say that for lattices $L,M$ and $N$
$$
L\oplus M \cong L\oplus N \Longrightarrow M\cong N.
$$
In other words, cancellation does not hold over $\mathbb{Z}$. …
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