Let G be a finite cover of a closed connected transpose-stable subgroup of GL(n,R) with complexified Lie algebra g. Let K be a maximal compact subgroup of G, and assume that G and K have equal rank. We prove a translation principle for the Dirac index of virtual (g,K)-modules. As a byproduct, to each coherent family of such modules, we attach a polynomial on the dual of the compact Cartan subal...

We introduce new families of pure quantum states that are constructed on top the well-known Gilmore-Perelomov group-theoretic coherent states. do this by constructing unitaries as exponential operators quadratic in Cartan subalgebra elements and applying these to regular This enables us generate entanglement not found themselves, while retaining many their desirable properties. Most importantly...

A Kac-Moody algebra is called hyperbolic if it corresponds to a generalized Cartan matrix of hyperbolic type. We study root subsystems of root systems of hyperbolic algebras. In this paper, we classify maximal rank regular hyperbolic subalgebras of hyperbolic Kac-Moody algebras. Introduction A generalized Cartan matrix A is called a matrix of hyperbolic type if it is indecomposable symmetrizabl...

In this paper, we apply the concept of t-norm T to fuzzy structure of B-algebras. The notion of a fuzzy B-subalgebra of B-algebras with respect to t-norm is introduced and several related properties are investigated. The direct product and T -product of T -fuzzy subalgebra of B-algebra is investigated.

In a 1991 paper, R. Mercer asserted that a Cartan bimodule isomorphism between Cartan bimodule algebras A1 and A2 extends uniquely to a normal ∗-isomorphism of the von Neumann algebras generated by A1 and A2 (Corollary 4.3 of Mercer, 1991). Mercer’s argument relied upon the Spectral Theorem for Bimodules of Muhly, Saito and Solel, 1988 (Theorem 2.5, there). Unfortunately, the arguments in the l...

In his article [3] in the Mathematical Intelligencer (vol. 11, no. 3) A. John Coleman gives a colorful biography of the mathematician Wilhelm Killing and offers an admiring appraisal of his paper [8]. The subject of this paper, the classification of the simple Lie algebras over C, has indeed turned out to be a milestone in the history of mathematics. At the conclusion of his article Coleman lis...

In this paper some properties of the uniformity topology on a BCI-algebras are discussed. Keywords—(Fuzzy) ideal, (Fuzzy) subalgebra, Uniformity, clopen sets.

In this paper we study composition series and em-beddings of Verma modules induced from "nonstandard" Borel subalgebras. This article can be viewed as a generalization of Futorny's work on imaginary Verma modules for Λ\ ' where the center of the Kac-Moody algebra acts nontrivially. Introduction. Let A be an indecomposable symmetrizable generalized Cartan matrix, fl(A) = n_ © f) 0 n+ the triangu...

This is a continuation of our previous paper studying the structure of Cartan subalgebras of von Neumann factors of type II1. We provide more examples of II1 factors having either zero, one or several Cartan subalgebras. We also prove a rigidity result for some group measure space II1 factors.

We introduce the notion of sensible fuzzy ideals of BCK-algebras with respect to a t-conorm and investigate some of their properties. We give the conditions for a sensible fuzzy subalgebra with respect to a t-conorm to be a sensible fuzzy ideal with respect to a t-conorm. Some properties of the direct product and S-product of fuzzy ideals of BCK-algebras with respect to a t-conorm are also disc...