By David Fisher

During this paper we produce an invariant for any ergodic, finite entropy motion of a lattice in an easy Lie staff on a finite degree area. The invariant is largely an equivalence category of measurable quotients of a undeniable kind. The quotients are primarily double coset areas and are created from a Lie crew, a compact subgroup of the Lie staff, and a commensurability type of lattices within the Lie workforce.

**Read Online or Download A canonical arithmetic quotient for actions of lattices in simple groups PDF**

**Similar symmetry and group books**

Over the last 30 years the idea of finite teams has constructed dramatically. Our realizing of finite uncomplicated teams has been better via their category. many questions about arbitrary teams could be diminished to related questions on uncomplicated teams and functions of the speculation are commencing to look in different branches of arithmetic.

- Group Representations: Background Material
- Felix Klein and Sophus Lie
- Picard groups of moduli problems
- Burnside Groups
- Seminaire Sophus Lie

**Extra resources for A canonical arithmetic quotient for actions of lattices in simple groups**

**Example text**

Conversely, assume a comaximal relation (6).

If P/JP is free over R/J , where J is the Jacobson radical of R, show that P is free over R. ) 12∗ . (Kaplansky [58]) Let P be a projective module over a local ring. Show that any element of P can be embedded in a free direct summand of P; deduce that every projective module over a local ring is free. 1 hold in most rings normally encountered, and counter-examples belong to the pathology of the subject. By contrast, the property defined below forms a significant restriction on the ring. Clearly any stably free module is finitely generated projective.

E. A = (0, I)P, B = P −1 (0, I)T . If we replace A, B by A P −1 , P B, we obtain C 0 0 A1 = 0 I A2 I B1 B2 0 . I On multiplying out, we find that A2 = 0, B2 = 0, C = A1 B1 and now the conclusion follows by induction. A square matrix C will be called a stable matrix atom if C ⊕ Ir is an atom for all r ≥ 1. 6. Over an Hermite ring every matrix atom is stable. We can specialize our ring still further. A ring R is called cancellable if for any projective modules P, Q, P ⊕ R ∼ = Q ⊕ R implies P ∼ = Q.