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Publications (17)

math.QA2001

Jordanian quantum spheres

R. Chakrabarti, J. Segar

We introduce and investigate a one parameter family of quantum spaces invariant under the left (right) coactions of the group-like element $T_{h}^{(j = 1)}$ of the Jordanian f…

math-ph2026

Affine extensions of $Z_{2}^{2}$ -graded $os p (1∣2)$ and Virasoro algebra

N. Aizawa, J. Segar

It is known that there are two inequivalent $Z_{2}^{2}$ -graded $os p (1∣2)$ Lie superalgebras. Their affine extensions are investigated and it is shown that one of them admits t…

math.QA2003

Super-Jordanian Quantum Superalgebra $U_{h} (os p (2/1))$

N. Aizawa, R. Chakrabarti, J. Segar

A triangular quantum deformation of $os p (2/1)$ from the classical $r$ -matrix including an odd generator is presented with its full Hopf algebra structure. The deformation maps, t…

math-ph2018

$Z_{2} \times Z_{2}$ generalizations of $N = 1$ superconformal Galilei algebras and their representations

N. Aizawa, P. S. Isaac, J. Segar

We introduce two classes of novel color superalgebras of $Z_{2} \times Z_{2}$ grading. This is done by realizing members of each in the universal enveloping algebra…

hep-th1996

Order-chaos transitions in field theories with topological terms: a dynamical systems approach

C. Mukku, M. S. Sriram, J. Segar +2

We present a comparative study of the dynamical behaviour of topological systems of recent interest, namely the non-Abelian Chern-Simons Higgs system and the Yang-Mills Chern-Simon…

math.QA2006

Universal T-matrix, Representations of OSp_q(1/2) and Little Q-Jacobi Polynomials

N. Aizawa, R. Chakrabarti, S. S. Naina Mohammed +1

We obtain a closed form expression of the universal T-matrix encapsulating the duality of the quantum superalgebra U_q[osp(1/2)] and the corresponding supergroup OSp_q(1/2). The cl…

cond-mat.stat-mech2013

Adiabatic thermostatistics of the two parameter entropy and the role of Lambert's W-function in its applications

R. Chandrashekar, J. Segar

A unified framework to describe the adiabatic class of ensembles in the generalized statistical mechanics based on Schwammle-Tsallis two parameter (q, q') entropy is proposed. The…

math-ph2016

Aspects of infinite dimensional $ℓ$ -super Galilean conformal algebra

N. Aizawa, J. Segar

In this work we construct a infinite dimensional $ℓ$ -super Galilean conformal algebra, which is a generalization of the $ℓ = 1$ algebra found in the literature. We give a class…

math.QA1998

Maps and twists relating $U (s l (2))$ and the nonstandard $U_{h} (s l (2))$ : unified construction

B. Abdesselam, A. Chakrabarti, R. Chakrabarti +1

A general construction is given for a class of invertible maps between the classical $U (s l (2))$ and the Jordanian $U_{h} (s l (2))$ algebras. Different maps are directly useful in dif…

math-ph2020

$Z_{2} \times Z_{2}$ generalizations of infinite dimensional Lie superalgebra of conformal type with complete classification of central extensions

N. Aizawa, P. S. Isaac, J. Segar

We introduce a class of novel $Z_{2} \times Z_{2}$ -graded color superalgebras of infinite dimension. It is done by realizing each member of the class in the universal…

math.RT2026

Graded Casimir Elements and Central Extensions of Color Lie Algebras

Naruhiko Aizawa, N. Aizawa, Ichi Fujii +5

A color Lie algebra is a generalization of a Lie (super)algebra by an Abelian group $Γ$ . The underlying vector space and defining relations of the algebra are graded by $Γ$ , and a…

quant-ph2005

Generalized boson algebra and its entangled bipartite coherent states

N. Aizawa, R. Chakrabaarti, J. Segar

Starting with a given generalized boson algebra U_<q>(h(1)) known as the bosonized version of the quantum super-Hopf U_q[osp(1/2)] algebra, we employ the Hopf duality arguments to…

math.QA2007

Basic Hypergeometric Functions and Covariant Spaces for Even Dimensional Representations of U_q[osp(1/2)]

N. Aizawa, R. Chakrabarti, S. S. Naina Mohammed +1

Representations of the quantum superalgebra U_q[osp(1/2)] and their relations to the basic hypergeometric functions are investigated. We first establish Clebsch-Gordan decompositio…

cond-mat.stat-mech2013

A Fractional entropy in Fractal phase space: properties and characterization

R. Chandrashekar, C. Ravikumar, J. Segar

A two parameter generalization of Boltzmann-Gibbs-Shannon entropy based on natural logarithm is introduced. The generalization of the Shannon-Kinchinn axioms corresponding to the t…

quant-ph2016

Distribution of quantum coherence in multipartite systems

R. Chandrashekar, P. Manikandan, J. Segar +1

The distribution of coherence in multipartite systems in examined. We use a new coherence measure with entropic nature and metric properties, based on the quantum Jensen-Shannon di…

math-ph2017

$Z_{2} \times Z_{2}$ generalizations of $N = 2$ super SchrÃ¶dinger algebras and their representations

N. Aizawa, J. Segar

We generalize the real and chiral $N = 2$ super SchrÃ¶dinger algebras to $Z_{2} \times Z_{2}$ -graded Lie superalgebras. This is done by $D$ -module presentat…

math-ph2013

Intertwining operators for l-conformal Galilei algebras and hierarchy of invariant equations

N. Aizawa, Y. Kimura, J. Segar

l-Conformal Galilei algebra, denoted by g{l}{d}, is a non-semisimple Lie algebra specified by a pair of parameters (d,l). The algebra is regarded as a nonrelativistic analogue of t…

Publications (17)

Jordanian quantum spheres

Affine extensions of Z22​-graded osp(1∣2) and Virasoro algebra

Super-Jordanian Quantum Superalgebra Uh​(osp(2/1))

Z2​×Z2​ generalizations of N=1 superconformal Galilei algebras and their representations

Order-chaos transitions in field theories with topological terms: a dynamical systems approach

Universal T-matrix, Representations of OSp_q(1/2) and Little Q-Jacobi Polynomials

Adiabatic thermostatistics of the two parameter entropy and the role of Lambert's W-function in its applications

Aspects of infinite dimensional ℓ-super Galilean conformal algebra

Maps and twists relating U(sl(2)) and the nonstandard Uh​(sl(2)): unified construction

Z2​×Z2​ generalizations of infinite dimensional Lie superalgebra of conformal type with complete classification of central extensions

Graded Casimir Elements and Central Extensions of Color Lie Algebras

Generalized boson algebra and its entangled bipartite coherent states

Basic Hypergeometric Functions and Covariant Spaces for Even Dimensional Representations of U_q[osp(1/2)]

A Fractional entropy in Fractal phase space: properties and characterization

Distribution of quantum coherence in multipartite systems

Z2​×Z2​ generalizations of N=2 super SchrÃ¶dinger algebras and their representations

Intertwining operators for l-conformal Galilei algebras and hierarchy of invariant equations

Affine extensions of $Z_{2}^{2}$ -graded $os p (1∣2)$ and Virasoro algebra

Super-Jordanian Quantum Superalgebra $U_{h} (os p (2/1))$

$Z_{2} \times Z_{2}$ generalizations of $N = 1$ superconformal Galilei algebras and their representations

Aspects of infinite dimensional $ℓ$ -super Galilean conformal algebra

Maps and twists relating $U (s l (2))$ and the nonstandard $U_{h} (s l (2))$ : unified construction

$Z_{2} \times Z_{2}$ generalizations of infinite dimensional Lie superalgebra of conformal type with complete classification of central extensions

$Z_{2} \times Z_{2}$ generalizations of $N = 2$ super SchrÃ¶dinger algebras and their representations