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P. G. Romeo

Publications and source records attributed to P. G. Romeo.

14 recordsLinked to original sources
arXiv2026

Cross-connections of the normed algebra of finite rank bounded operators on a Hilbert space

In this article we examine the cross-connections of the normal category of finite dimensional subspaces of a Hilbert space and it's dual space. Further, we describe the cross-connection semigroup of cones, which is a normed algebra isomrphic to the normed algebra of finite rank bounded operators on a Hilbert space. We also characterize compact operators and their spectrum by the normal cones in the normal category of proper subspaces of a Hilbert space.

math.FA↗
arXiv2026

Ordered semigroups and ideal categories of principal ideal rings

In this paper, we view the collection of ideals of a commutative principal ideal ring from two perspectives: one as an ordered semigroup I(R) and the other as a category I_R . It is shown that I(R) is a regular ordered semigroup whereas I_R is a category with subobjects. Further we establish the correspondence between these structure

math.RA↗
arXiv2024

Cross-connection semigroups amalgam of a vector bundle

Cross-connections of normal categories was introduced by K.S.S.Nambooripad while discussing the structure of regular semigroups and via this cross-connections he obtained a beautiful representetion of regualr semigroup called the cross-connection semigroup (see cf.[4]). Subsequently cross-connection representation of various other semigroups such as concordant semigroups, semigroup of endomorphisms of a vector space are also described (cf.[6][5]). In this paper we describe the semigroup amalgam of cross-connection semigroups of the fibers of a vector bundle.

math.CT↗
arXiv2023

Irreducible representation of Plesken Lie algebras

Cohen and Taylor introduced Plesken Lie algebra as certain Lie algebra constructed using finite groups. Arjun and Romeo described the linear representation of these Lie algebras induced from group representation in [1]. Hence the authors posed the question as to what are the irreducible representations of Plesken Lie algebras and describes the irreducible representations of cover of Plesken Lie algebras.

math.RT↗
arXiv2023

Some ordered matrix semigroups

A semigroup together with compatible partial order is called an odered semigroup. In this paper we discuss the ordered matrix semigroups.

math.GR↗
arXiv2022

Representation of Plesken Lie algebras

Cohen and Taylor introduced Plesken Lie algebras of finite groups and studied their structural properties. As a further step, we will introduce Plesken Lie algebra representations, Plesken Lie algebra modules and discuss the irreducibility property.

math.RT↗
arXiv2021

Chain Bundles and Category of Chains

In [7], we introduced the category of chain bundles with examples and established its significance. Here we shall describe certain categories which we call the category of chains in the chain bundle category and discuss some interesting categorical properties of this chain categories

math.CT↗
arXiv2020

Generalized groups and module groupoids

In this paper we discuss generalized group, provides some interesting examples. Further we introduce a generalized module as a module like structure obtained from a generalized group and discuss some of its properties and we also describes generalized module groupoids.

math.GM↗
arXiv2020

Biordered sets of lattices and homogeneous basis

In this paper we discuss the properties of the biordered set obtained from a complemented modular lattice and defines an operation using the sandwich elements of the biordered set. Further we describe a biordered subset satisfying certain conditions, so that the complemented modular lattice admits a homogeneous basis. Finally analogous to von Neumann coordinatization theorem we describe the coordinatization theorem for complemented modular lattice using the biordered set of idempotents.

math.RA↗
arXiv2019

Local subsemigroups and variants of some class of semigroups

For an element a in a semigroup S the local subsemigroup of S with respect to a is the subsemigroup aSa of S and the variant of S with respect to a is a semigroup with underlying set S with a sandwich operation xy = xay for all x, y in S. In this paper we discuss the structures of local subsemigroups of full transformation semigroups and symmetric inverse monoids. It is also shown that the set of all local subsemigroups of finite symmetric inverse monoids and the set of all variants of all finite symmetric inverse monoids are same upto isomorphism.

math.GR↗
arXiv2019

Ideal categories of rings and ring of cones

In this paper we describe the ideal category of a ring R as preadditive proper category. Further it is also shown that the cones in this category is a ring with appropriate addition and multiplication.

math.CT↗
arXiv2019

Directed Graphs of Cayley Functions

In this paper we describe a condition under which a given function that commute with an idempotent function on an infinite set is a Cayley function using its functional digraph.

math.RA↗
arXiv2019

Cross-connection structure of concordant semigroups

Cross-connection theory provides the construction of a semigroup from its ideal structure using small categories. A concordant semigroup is an idempotent-connected abundant semigroup whose idempotents generate a regular subsemigroup. We characterize the categories arising from the generalised Green relations in the concordant semigroup as consistent categories and describe their interrelationship using cross-connections. Conversely, given a pair of cross-connected consistent categories, we build a concordant semigroup. We use this correspondence to prove a category equivalence between the category of concordant semigroups and the category of cross-connected consistent categories. In the process, we illustrate how our construction is a generalisation of Nambooripad's cross-connection analysis of regular semigroups. We also identify the inductive cancellative category associated with a pair of cross-connected consistent categories.

math.GR↗