arithmetic lattice造句
例句與造句
- S-arithmetic lattice ( where S stands for the set of primes inverted ).
- Generalising the construction above one gets the notion of an " arithmetic lattice " in a semisimple Lie group.
- All arithmetic lattices in \ mathrm { SL } _ 2 ( \ mathbb R ) are obtained in this way ( up to commensurability ).
- Instead of taking intergal points in the definition of an arithmetic lattice one can take points which are only integral away from a finite number of primes.
- The conjecture ( usually attributed to Jean-Pierre Serre is that this is true for ( irreducible ) arithmetic lattices in higher-rank groups and false in rank-one groups.
- It's difficult to find arithmetic lattice in a sentence. 用arithmetic lattice造句挺難的
- By work of Klingler ( also proved independently by Yeung ) all such are quotients of the 2-ball by arithmetic lattices in \ mathrm { PU } ( 2, 1 ).
- The terminology introduced above is coherent with this, as a theorem due to Borel and Harish-Chandra states that an arithmetic lattice in a semisimple Lie group is of finite covolume ( the discreteness is obvious ).
- The theorem is more precise : it tells that the arithmetic lattice is cocompact if and only if the " form " of G used to define it ( i . e . the \ mathbb Q-group \ mathrm G ) is anisotropic.
- For example, the arithmetic lattice associated to a quadratic form in n variables over \ mathbb Q will be co-compact in the associated orthogonal group if and only if the quadratic form does not vanish at any point in \ mathbb Q ^ n \ setminus \ { 0 \ }.
- This work recovers in the classical case the finiteness of Takeuchi's list, and by means of a characterisation of the lattices they construct that are arithmetic groups, provided new examples of non-arithmetic lattices in " PU " ( 1, " n " ).
- A conjecture generally attributed to Serre states that an irreducible arithmetic lattice in a semisimple Lie group G has the congruence subgroup property if and only if the real rank of G is at least 2; for example, lattices in \ mathrm { SL } _ 3 ( \ mathbb R ) should always have the property.
- For every semisimple Lie group G it is in theory possible to classify ( up to commensurability ) all arithmetic lattices in G, in a manner similar to the cases G = \ mathrm { SL } _ 2 ( \ mathbb R ), \, \ mathrm { SL } _ 2 ( \ mathbb C ) explained above.
- When G is a Lie group one can define an arithmetic lattice in G as follows : for any algebraic groups \ mathrm G defined over \ mathbb Q such that there is a morphism \ mathrm G ( \ mathbb R ) \ to G with compact kernel, the image of an arithmetic subgroup in \ mathrm G ( \ mathbb Q ) is an arithmetic lattice in G.
- When G is a Lie group one can define an arithmetic lattice in G as follows : for any algebraic groups \ mathrm G defined over \ mathbb Q such that there is a morphism \ mathrm G ( \ mathbb R ) \ to G with compact kernel, the image of an arithmetic subgroup in \ mathrm G ( \ mathbb Q ) is an arithmetic lattice in G.