Varieties of Complete Pairs of Zero-Dimensional Subschemes of Lengths ≥2 and ≥4 in Algebraic Surfaces

We prove that the varieties of complete pairs of zero-dimensional subschemes of lengths d ₁ 2, d ₂ 4 on a smooth irreducible projective algebraic surface are singular.     

Axiom A flows with a transverse torus

Let be an Axiom A flow with a transverse torus exhibiting a unique orbit that does not intersect . Suppose that there is no null-homotopic closed curve in contained in either the stable or unstable set of . Then we show that has either an attracting periodic orbit or a repelling periodic orbit or is transitive. In particular, an Anosov flow with a transverse torus is transitive if it has a unique periodic orbit that does not intersect the torus.

     

Torus actions on symplectic orbi-spaces

Which -dimensional orbi-spaces have effective symplectic - torus actions? As shown by Lerman and Tolman (1997) and Watson (1997), this question reduces to that of characterizing the finite subgroups of centralizers of tori in the real symplectic group . We resolve this question, and generalize our method to a calculation of the centralizers of all tori in .

     

Stability of a Special Class of $$q_{ij}$$ -CCR and Extensions of Higher-Dimensional Noncommutative Tori

The -algebras A_{{q i}}, generated by generalised quon commutation relations are considered. The nuclearity of these algebras is proved. It is shown that A_{{q i}}, is isomorphic to the extension of a higher-dimensional noncommutative torus. Irreducible representations of A_{{q i}}, are considered. It is shown that the Fock representation is faithful.     

Abelian Subgroups of Garside Groups

In this article, we show that for every abelian subgroup H of a Garside group, some conjugate g ^?1 Hg consists of ultra summit elements and the centralizer of H is a finite index subgroup of the normalizer of H. Combining with the results on translation numbers in Garside groups, we obtain an easy proof of the algebraic flat torus theorem for Garside groups and solve several algorithmic problems concerning abelian subgroups of Garside groups.     

（n-3）-Filiform李代数的极大环面

求出了（n-3）-filiform李代数的极大环面，并证明了（n-3）-filiform李代数是可完备化的．     

Enumeration of Mapping Classes for the Torus

We enumerate periodic, reducible, and Anosov elements of the mapping class group of the torus, and determine their growth function. Then we prove that almost all elements of the mapping class group of the torus are Anosov.     

Total destruction of Lagrangian tori

For an integrable Tonelli Hamiltonian with d   (d?2$d?2$) degrees of freedom, we show that all of the Lagrangian tori can be destroyed by analytic perturbations which are arbitrarily small in the C^d−δ$C^{d-\delta }$ topology.     

LENTICULAR NONCOMMUTATIVE TORI

All C*-algebras of sections of locally trivial C* -algebra bundles over ∏i=1sLki(ni) with fibres Aw Mc(C) are constructed, under the assumption that every completely irrational noncommutative torus Aw is realized as an inductive limit of circle algebras, where Lki (ni) are lens spaces. Let Lcd be a cd-homogeneous C*-algebra over whose cd-homogeneous C*-subalgebra restricted to the subspace Tr × T2 is realized as C(Tr) A1/d Mc(C), and of which no non-trivial matrix algebra can be factored out.The lenticular noncommutative torus Lpcd is defined by twisting in by a totally skew multiplier p on Tr+2 × Zm-2. It is shown that is isomorphic to if and only if the set of prime factors of cd is a subset of the set of prime factors of p, and that Lpcd is not stablyisomorphic to if the cd-homogeneous C*-subalgebra of Lpcd restricted to some subspace LkiLki (ni) is realized as the crossed product by the obvious non-trivial action of Zki on a cd/ki-homogeneous C*-algebra over S2ni+1 for ki an integer greater than