Amit Kuber

activity

20202025

collaborators

9 papers

math.LO2025

Model-theoretic $K_{1}$ for modules over semisimple rings: (weak) Morita invariance

Sourayan Banerjee, Amit Kuber

This paper is a sequel to a paper by the same authors, where they defined $K$ -groups of model-theoretic structures, and computed $K_{1}$ of free modules over PIDs. In this paper, we…

math.RT2025

Generalised tree modules: Hom-sets and indecomposability

Annoy Sengupta, Amit Kuber

For a zero-relation algebra over a field $K$ , Crawley-Boevey introduced the concept of a tree module and provided a combinatorial description of a basis for the space of h…

math.LO2024

Model-theoretic $K_{1}$ of free modules over PIDs

Sourayan Banerjee, Amit Kuber

Motivated by Krajiček and Scanlon's definition of the Grothendieck ring $K_{0} (M)$ of a first-order structure $M$ , we introduce the definition of $K$ -groups $K_{n} (M)$ for $n \geq 0$ via…

math.RT2024

Characterisation of band bricks over certain string algebras and a variant of perfectly clustering words

Annoy Sengupta, Amit Kuber

Generalising a recent work of Dequêne et al. on the connection between perfectly clustering words and band bricks over a particular family of gentle algebras, we characterise band…

math.RA2023

A note on injectivity of monomial algebras

Ardeline M. Buhphang, Rishabh Goswami, Amit Kuber

We show that a monomial algebra $Λ$ over an algebraically closed field $K$ is self-injective if and only if each map $soc (_{Λ} Λ) \to_{Λ} Λ$ can be extended to an endomorphism…

math.RT2023

Hammocks for non-domestic string algebras

Vinit Sinha, Amit Kuber, Annoy Sengupta +1

We show that the order type of the simplest version of a hammock for string algebras lies in the class of finite description linear orders--the smallest class of linear orders cont…

math.RT2022

On the computation of order types of hammocks for domestic string algebras

Shantanu Sardar, Amit Kuber

For the representation-theoretic study of domestic string algebras, Schröer introduced a version of hammocks that are bounded discrete linear orders. He introduced a finite combina…

math.RT2021

Variations of the bridge quiver for domestic string algebras

Shantanu Sardar, Amit Kuber

In the computation of some representation-theoretic numerical invariants of domestic string algebras, a finite combinatorial gadget introduced by Schröer--the \emph{bridge quiver}…

math.RT2020

On the stable radical of some non-domestic string algebras

Esha Gupta, Amit Kuber, Shantanu Sardar

We introduce the concept of a prime band in a string algebra $Λ$ and use it to associate to $Λ$ its finite bridge quiver. Then we introduce a new technique of `recursive systems' f…

Model-theoretic K1​ for modules over semisimple rings: (weak) Morita invariance