- polyhedron. This is why d( Λ {\displaystyle \Lambda } ) is
sometimes called the
covolume of the lattice. If this
equals 1, the
lattice is
called unimodular. Minkowski's...
- {\displaystyle 2^{n}\,d(L)} ,
where d ( L ) {\displaystyle d(L)}
denotes the
covolume of the
lattice (the
absolute value of the
determinant of any of its bases)...
- Mahler's
theorem is
equivalent to the
compactness of the
space of unit-
covolume lattices in R n {\displaystyle \mathbb {R} ^{n}}
whose systole is larger...
-
finite type. A
Kleinian group Γ has
finite covolume if H3/Γ has
finite volume. Any
Kleinian group of
finite covolume is
finitely generated. A
Kleinian group...
- of the n-dimensional
parallelepiped the set
subtends (also
called the
covolume of the lattice). This
parallelepiped is a
fundamental region of the symmetry:...
- BTB is the
discriminant of O. The
discriminant is
denoted Δ or D. The
covolume of the
image of O is | Δ | {\displaystyle {\sqrt {|\Delta |}}} . Real and...
- **** and
others on
algebraic groups.
Shortly afterwards the
finiteness of
covolume was
proven in full
generality by
Borel and Harish-Chandra. Meanwhile, there...
-
covolume,
where G is a
semisimple algebraic group over the reals. This is in
contrast to a lattice,
which is a
discrete subgroup of
finite covolume....
- of P,
divided by d(L) (see
lattice for an
explanation of the
content or
covolume d(L) of a lattice); the
second coefficient, L d − 1 ( P ) {\displaystyle...
- {\displaystyle \gamma _{n}} For a
lattice L in
Euclidean space Rn with unit
covolume, i.e. vol(Rn/L) = 1, let λ1(L)
denote the
least length of a
nonzero element...
