We revisit the characterisation of modules over non-unital C∗-algebras analogous to modules of sections of vector bundles. A fullness condition on the associated multiplier module characterises a class of modules which closely mirror the commutative case. We also investigate the multiplier-module construction in the context of bi-Hilbertian bimodules, particularly those of finite numerical inde...

This paper focuses on completeness results about generic expansions of logics of both continuous t-norms and Weak Nilpotent Minimum (WNM) with truth-constants. Indeed, we consider algebraic semantics for expansions of these logics with a set of truth-constants {r | r ∈ C}, for a suitable countable C ⊆ [0, 1], and provide a full description of completeness results when (i) either the t-norm is a...

For a relative exact homological category (C,E), we define relative points over an arbitrary object in C, and show that they form an exact homological category. In particular, it follows that the full subcategory of nilpotent objects in an exact homological category is an exact homological category. These nilpotent objects are defined with respect to a Birkhoff subcategory in C as defined by T....

For a regular sub-Riemannian manifold we study the Radon-Nikodym derivative of the spherical Hausdorff measure with respect to a smooth volume. We prove that this is the volume of the unit ball in the nilpotent approximation and it is always a continuous function. We then prove that up to dimension 4 it is smooth, while starting from dimension 5, in corank 1 case, it is C (and C on every curve)...

Throughout this paper, R is an associative ring; andN ,C,C(R), and J denote, respectively, the set of nilpotent elements, the center, the commutator ideal, and the Jacobson radical. An element x of R is called potent if xn = x for some positive integer n= n(x) > 1. A ring R is called periodic if for every x in R, xm = xn for some distinct positive integersm=m(x), n = n(x). A ring R is called we...

We reduce the graph isomorphism problem to 2-nilpotent p-groups isomorphism problem (and to finite 2-nilpotent Lie algebras the ring Z/pZ. Furthermore, we show that classifying problems in categories graphs, finite 2-nilpotent p-groups, and 2-nilpotent Lie algebras over Z/pZ are polynomially equivalent and wild.

In the first part, we prove that the dominion (in the sense of Isbell) of a subgroup of a finitely generated nilpotent group is trivial in the category of all nilpotent groups. In the second part, we show that the dominion of a subgroup of a finitely generated nilpotent group of class two is trivial in the category of all metabelian nilpotent groups. Section

Abstract. Let G be a reductive algebraic group over C and let N be a G-module. For any subspace M of N , the Brylinski-Kostant filtration on M is defined through the action of a principal nilpotent element in LieG. This filtration is related to a q-analog of weight multiplicity due to Lusztig. We generalize this filtration to other nilpotent elements and show that this generalized filtration is...

Let G be a complex symplectic group. In [K1], we singled out the nilpotent cone N of some reducible G-module, which we call the (1-) exotic nilpotent cone. In this paper, we study the set of G-orbits of the variety N. It turns out that the variety N gives a variant of the Springer correspondence for Weyl groups of type C, but shares a similar flavor with that of type A case. (I.e. there appears...

An absolute parallelism for $2$-nondegenerate CR manifolds $M$ of hypersurface type was recently constructed independently by Isaev-Zaitsev, Medori-Spiro, and Pocchiola in the minimal possible dimension ($\dim M=5$), $\dim M=7$ certain cases first author. We develop a bigraded analog Tanaka's prolongation procedure to construct canonical these structures arbitrary (odd) with Levi kernel admissi...