In the present note, which is second part of a work concerning study set symmetric states, we introduce extension Klein transformation for general Fermi tensor product two $\bz^2$ graded $C^*$-algebras, under condition that grading one involved algebras inner. After extending construction to $C^*$-inductive limits, such realises canonical $*$-isomorphism between $\bz^2$-graded $C^*$-algebras ma...

Let (X , x0) be any one–pointed compact connected Riemann surface of genus g, with g ≥ 3. Fix two mutually coprime integers r > 1 and d. Let MX denote the moduli space parametrizing all logarithmic SL(r, C)–connections, singular over x0, on vector bundles over X of degree d. We prove that the isomorphism class of the variety MX determines the Riemann surface X uniquely up to an isomorphism, alt...

In [24], confirming a conjecture of Hjorth-Kechris [16], Thomas-Velickovic proved that the isomorphism relation on the space Gfg of finitely generated groups is a universal countable Borel equivalence relation. (Here Gfg denotes the Polish space of finitely generated groups introduced by Grigorchuk [12]; i.e. the elements of Gfg are the isomorphism types of marked groups (G, c ), where G is a f...

Nonhomeomorphic compact Hausdorff spaces X and Y and an isomorphism : C(X) -> C(Y) (onto) are constructed such that ||c/>|| \4>~ || = 2. Amir had asked if such a d> exists with || \\ ||cf> || < 3.

polygroups are multivalued systems that satisfy group like axioms. in this paper the class of n-arypolygroups is introduced. the concepts of n-ary normal subpolygroups and strong homomorphisms of n-arypolygroups are adopted. with respect to these concepts the isomorphism theorems for n-ary polygroups arestated and proved. finally, we will consider the fundamental relation  * defined on an n-ar...

Given a reductive Lie algebra g and choice of Cartan subalgebra h, the HarishChandra map gives an isomorphism between the center z of the universal enveloping algebra U(g) of g and the algebra of Weyl group invariant symmetric tensors of h, denoted S(h) . We define these objects and give a sketch of the proof, using sl(2,C) as a motivating example. The proofs and examples mirror those found in ...