The column space of a real n× k matrix x of rank k is a k-plane. Thus we get a map from the space X of such matrices to the Grassmannian G of k-planes in Rn, and hence a GLn-equivariant isomorphism C∞ (G) ≈ C∞ (X)k . We consider the On ×GLk-invariant differential operator C on X given by C = det ( xx ) det ( ∂∂ ) , where x = (xij) , ∂ = ( ∂ ∂xij ) . By the above isomorphism C defines an On-inva...

Symplectic reduction is reinterpreted as the composition of arrows in the category of integrable Poisson manifolds, whose arrows are isomorphism classes of dual pairs, with symplectic groupoids as units. Morita equivalence of Poisson manifolds amounts to isomorphism of objects in this category. This description paves the way for the quantization of the classical reduction procedure, which is ba...

in this paper, the notion of fuzzy n-polygroups (fn -polygroups) is introduced and some related properties are investigated. in this regards, the concepts of normal  f-subpolygroups and homomorphisms of fn-polygroups are adopted. also, the quotient of fn-polygroups by defining regular relations are studied. finally, the classical isomorphism theorems of groups are generalized to fn-polygroups p...

We classify all essential extensions of the form $$ 0 \rightarrow \mathcal{B} \mathcal{D} C(X) where $\mathcal{B}$ is a nonunital, simple, separable, finite, real rank zero, $\mathcal{Z}$-stable $C^\*$-algebra with continuous scale, and $X$ finite CW complex. In fact, we prove that there group isomorphism \mathbf{Ext}(C(X), \mathcal{B}) KK(C(X), \mathcal{M}(\mathcal{B})/\mathcal{B}).

In 1996, Harris and Kadison posed the following problem: show that a linear bijection between C∗-algebras that preserves the identity and the set of invertible elements is a Jordan isomorphism. In this paper, we show that if A and B are semisimple Banach algebras andΦ : A→ B is a linear map onto B that preserves the spectrum of elements, thenΦ is a Jordan isomorphism if either A or B is a C∗-al...

We review the recent developement on the subject, emphasizing its analytic aspects and pointing out some open problems. The study of exotic C-s is at the very beginning, and hopefully this survey would be useful to learn more about these unusual and beautiful objects. All algebraic varieties considered below are usually assumed being smooth, reduced, irreducible, and defined over C. Isomorphism...

This paper denes and investigates the ergodic proper-ties of the entropy of a countable partition of a fuzzy dynamical sys-tem at different points of the state space. It ultimately introducesthe local fuzzy entropy of a fuzzy dynamical system and proves itto be an isomorphism invariant.

A function J defined on a family C of stationary processes is finitely observable if there is a sequence of functions sn such that sn(x1 . . . xn) → J(X ) in probability for every process X =(xn) ∈ C. Recently, Ornstein and Weiss proved the striking result that if C is the class of aperiodic ergodic finite valued processes, then the only finitely observable isomorphism invariant defined on C is...

In this paper, we first introduce the concepts of G-systems, quotient G-systems and isomorphism theorems on G-systems of n-ary semihypergroups . Also we consider the Green's equivalences on G-systems and further in-vestigate some of their properties. A number of n-ary semihypergroups are constructed and presented as examples in this paper.