Searcharxiv⌕ Search

arXiv subjects

B. Ransingh

Publications and source records attributed to B. Ransingh.

6 recordsLinked to original sources
arXiv2021

An Introduction to Supersymmetric Cluster Algebras

In this paper we propose the notion of cluster superalgebras which is a supersymmetric version of the classical cluster algebras introduced by Fomin and Zelevinsky. We show that the symplectic-orthogonal supergroup $SpO(2|1)$ admits a cluster superalgebra structure and as a consequence of this, we deduce that the supercommutative superalgebra generated by all the entries of a superfrieze is a subalgebra of a cluster superalgebra. We also show that the coordinate superalgebra of the super Grassmannian $G(2|0; 4|1)$ of chiral conformal superspace (that is, $(2|0)$ planes inside the superspace $\mathbb C^{4|1}$) is a quotient of a cluster superalgebra.

math.RA↗
arXiv2017

Splints of root systems on Lie Superalgebras

This paper classifies the splints of the root system of classical Lie superalgebras as a superalgebraic conversion of the splints of classical root systems. It can be used to derive branching rules, which have potential physical application in theoretical physics.

math-ph↗
arXiv2016

A quick proof of the classification of real Lie superalgebras

This article classifies the real forms of Lie Superalgebra by Vogan diagrams, developing Borel and de Seibenthal theorem of semisimple Lie algebras for Lie superalgebras. A Vogan diagram is a Dynkin diagram of triplet $(\mathfrak{g}_{C},\mathfrak{h_{\bar{0}}},\triangle^{+})$, where $\mathfrak{g}_{C}$ is a real Lie superalgebra, $\mathfrak{h_{\bar{0}}}$ cartan subalgebra, $\triangle^{+}$ positive root system. Although the classification of real forms of contragradient Lie superalgebras is already done. But our method is a quicker one to classify.

math.RT↗
arXiv2013

Defining relations and flip Dynkin superdiagrams

The motivation comes from boson fermion correspondence. This article shows for each fermionic root there is correspondence a bosonic root, as a result we get for each Dynkin diagram of Lie Superalgebra a corresponding flip Dynkin Superdiagram. This article construct all the filp Dynkin Superdiagrams of Lie superalgebras(LS). This can create non conjugate classes Borel subalgebra (subsuperalgebras) or non isomorphic Dynkin diagrams of LS using \inδsequences. We have got the defining relations for the both the Dynkin diagrams and flip Dynkin diagrams.

math-ph↗