The integral Gram determinant has absolute value one, equivalently the lattice equals its bilinear-form dual. The K3 intersection lattice is an indefinite example.
An integral quadratic lattice that is both an even lattice and a unimodular lattice. The K3 intersection lattice has signature , while the positive-definite E8 lattice has rank eight.
The positive-definite rank-eight even unimodular lattice can be realized as vectors in or whose coordinate sum is even, with the ordinary Euclidean inner product. Negating this form gives in the K3 intersection lattice.
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An unimodular lattice is a type of mathematical structure that arises in the context of lattice theory and algebraic geometry, particularly in the study of quadratic forms and integer lattices. Here are the key characteristics and definitions associated with unimodular lattices: 1. **Lattice**: A lattice in Euclidean space is a discrete subgroup of that space generated by a set of basis vectors.