The possible observability indices of an observable pair of matrices, when supplementary subpairs are prescribed, are characterized when the “quotient” one is nilpotent. The geometric techniques used are also valid in the classical Carlson problem for square matrices.

In this paper we study irreducible representations of regular limit subalgebras of AF-algebras. The main result is twofold: every closed prime ideal of a limit of direct sums of nest algebras (NSAF) is primitive, and every prime regular limit algebra is primitive. A key step is that the quotient of a NSAF algebra by any closed ideal has an AF C*-envelope, and this algebra is exhibited as a quot...

For each pair of coprime integers n > m ≥ 2 we construct pairs of non equivalent Conway irreducible hyperbolic knots with the same n-fold and m-fold cyclic branched covers. Mathematics Subject Classification (2000). Primary 57M25; Secondary 57M12, 57M50.

The ground field k is algebraically closed and of characteristic zero. Let g be a reductive algebraic Lie algebra over k and σ an involutory automorphism of g. Then g = g0 ⊕ g1 is the direct sum of σ-eigenspaces. Here g0 is a reductive subalgebra and g1 is a g0-module. Let G be the adjoint group of g and G0 ⊂ G a connected subgroup with LieG0 = g0. The commuting variety of (g, g0) is the follow...

let $r$ be a commutative ring. the purpose of this article is to introduce a new class of ideals of r called weakly irreducible ideals. this class could be a generalization of the families quasi-primary ideals and strongly irreducible ideals. the relationships between the notions primary, quasi-primary, weakly irreducible, strongly irreducible and irreducible ideals, in different rings, has bee...

We construct an A∞-category D(C|B) from a given A∞-category C and its full subcategory B. The construction is similar to a particular case of Drinfeld’s construction of the quotient of differential graded categories [Dri04]. We use D(C|B) to construct an A∞-functor of K-injective resolutions of a complex, when the ground ring is a field. The conventional derived category is obtained as the 0-th...

This paper studies aspects of the dynamics of a conventional mechanism of ligand-receptor interactions, with a focus on the stability and location of steady-states. A theoretical framework is developed, which is based upon the rich and deep formalism of irreducible biochemical networks. When represented in this manner, the mass action kinetics of biochemical processes can be clearly seen in ter...

Given an invariant J(K) of a knot K, the corresponding (1, 1)-tangle invariant J ′(K) = J(K)/J(U) is defined as the quotient of J(K) by its value J(U) on the unknot U . We prove here that J ′ is always an integer 2-variable Laurent polynomial when J is the Homfly satellite invariant determined by decorating K with any eigenvector of the meridian map in the Homfly skein of the annulus. Specialis...

We construct the entire generalized Kac-Moody Lie algebra as a quotient of the positive part of another generalized Kac-Moody Lie algebra. The positive part of a generalized Kac-Moody Lie algebra can be constructed from representations of quivers using Ringel's Hall algebra construction. Thus we give a direct realization of the entire generalized Kac-Moody Lie algebra. This idea arises from the...