Suppose that an algebraic torus G acts algebraically on a projective manifold X with generically trivial stabilizers. Then the Zariski closure of the set of pairs {(x, y) ∈ X × X | y = gx for some g ∈ G} defines a nonzero equivariant cohomology class [∆G] ∈ H G×G(X×X). We give an analogue of this construction in the case where X is a compact symplectic manifold endowed with a hamiltonian action...

For a compact space X we consider extending endomorphisms of the algebra C(X) to be endomorphisms of Arens-Hoffman and Cole extensions of C(X). Given a non-linear, monic polynomial p ∈ C(X)[t], with C(X)[t]/pC(X)[t] semi-simple, we show that if an endomorphism of C(X) extends to the Arens-Hoffman extension with respect to p then it also extends to the simple Cole extension with respect to p. We...

Just as knots and links can be algebraically described as certain morphisms in the category of tangles in 3 dimensions, compact surfaces smoothly embedded in R4 can be described as certain 2-morphisms in the 2-category of ‘2-tangles in 4 dimensions’. Using the work of Carter, Rieger and Saito, we prove that this 2-category is the ‘free semistrict braided monoidal 2-category with duals on one un...

let g be a locally compact group, and let ω be a weight on g. we show that the weightedmeasure algebra m(g,ω) is amenable if and only if g is a discrete, amenable group andsup{ω(g) ω(g−1) : g ∈ g} < ∞, where ω(g) ≥ 1 (g ∈ g) .

We determine the number of isomorphism classes elementary gradings by a finite group on an algebra upper block-triangular matrices. As consequence we prove that, for abelian G , sequence numbers E ( m ) -gradings M F × matrices with entries in field characterizes . A formula over algebraically closed field, mild restrictions its characteristic, is also provided. Finally, if group, and N that ∼ ...

Just as knots and links can be algebraically described as certain morphisms in the category of tangles in 3 dimensions, compact surfaces smoothly embedded in R4 can be described as certain 2-morphisms in the 2-category of ‘2-tangles in 4 dimensions’. Using the work of Carter, Rieger and Saito, we prove that this 2-category is the ‘free semistrict braided monoidal 2-category with duals on one un...

In this paper we answer a question raised in [Mol] by giving an example of a proper standard C∗-subalgebra of B(H) whose automorphism and isometry groups are topologically reflexive. After this we prove that in the case of extensions of the C∗-algebra C(H) of all compact operators by separable commutative C∗algebras, these groups are algebraically reflexive. Concerning the most well-known exten...

Let A be a hereditary algebra over an algebraically closed field k andA(m) be them-replicated algebra of A. Given an A(m)-module T , we denote by δ(T ) the number of non isomorphic indecomposable summands of T . In this paper, we prove that a partial tilting A(m)module T is a tilting A(m)-module if and only if δ(T ) = δ(A(m)), and that every partial tilting A(m)-module has complements. As an ap...

The concept of ‘topological right transversal’ is introduced to study right transversals in topological groups. Given any right quasigroup S with a Tychonoff topology T , it is proved that there exists a Hausdorff topological group in which S can be embedded algebraically and topologically as a right transversal of a subgroup (not necessarily closed). It is also proved that if a topological rig...