arXiv subjects

Surajit Biswas

Publications and source records attributed to Surajit Biswas.

10 recordsLinked to original sources

arXiv2026

Topological invariance of quantum homogeneous spaces of type $B$ and $D$

In this article, we study two families of quantum homogeneous spaces, namely, $SO_q(2n+1)/SO_q(2n-1)$, and $SO_q(2n)/SO_q(2n-2)$. By applying a two-step Zhelobenko branching rule, we show that the $C^*$-algebras $C(SO_q(2n+1)/SO_q(2n-1))$, and $C(SO_q(2n)/SO_q(2n-2))$ are generated by the entries of the first and the last rows of the fundamental matrix of the quantum groups $SO_q(2n+1)$, and $SO_q(2n)$, respectively. We then construct a chain of short exact sequences, and using that, we compute $K$-groups of these spaces with explicit generators. Invoking homogeneous $C^*$-extension theory, we show $q$-independence of some intermediate $C^*$-algebras arising as the middle $C^*$-algebra of these short exact sequences. As a consequence, we get the $q$-invariance of $SO_q(3)$, $SO_q(5)/SO_q(3)$, $SO_q(4)/SO_q(2)$, and $SO_q(6)/SO_q(4)$.

math.QA↗

arXiv2025

Spectral dimension of $p$-adic integers

The notion of spectral dimension was introduced by Chakraborty and Pal in \cite{cp}. In this paper, we show that the spectral dimension of the ring of $p$-adic integers, $\mathbb{Z}_p$, is equal to its manifold dimension, which is $0$. Finally, we determine the $K$-groups of $\mathbb{Z}_p$, and show that the generators of $K_0(\mathbb{Z}_p)$ can be expressed as finite span of the characters of $\mathbb{Z}_p$.

math.QA↗

arXiv2025

On the classification of $C^*$-algebras of twisted isometries with finite dimensional wandering spaces

Let $ m, n \in \mathbb{N}_0 $, and let $ X $ be a closed subset of $ \mathbb{T}^{\binom{m+n}{2}} $. We define $ C^{m,n}_X $ to be the universal $ C^* $-algebra among those generated by $ m $ unitaries and $ n $ isometries satisfying doubly twisted commutation relations with respect to a twist $ \mathcal{U} = \{U_{ij}\}_{1 \leq i < j \leq m+n} $ of commuting unitaries having joint spectrum $ X $. We provide a complete list of the irreducible representations of $ C^{m,n}_X $ up to unitary equivalence and, under a denseness assumption on $ X $, explicitly construct a faithful representation of $ C^{m,n}_X $. Under the same assumption, we also give a necessary and sufficient condition on a fixed tuple $ \mathcal{U} $ of commuting unitaries with joint spectrum $ X $ for the existence of a universal tuple of $ \mathcal{U} $-doubly twisted isometries. For $ X = \mathbb{T}^{\binom{m+n}{2}} $, we compute the $ K $-groups of $ C^{m,n}_X $. We further classify the $ C^* $-algebras generated by a pair of doubly twisted isometries with a fixed parameter $ θ\in \mathbb{R} \setminus \mathbb{Q} $, whose wandering spaces are finite-dimensional. Finally, for a fixed unitary $ U $, we classify all the $ C^* $-algebras generated by a pair of $ U $-doubly twisted isometries with finite-dimensional wandering spaces.

math.OA↗

arXiv2025

Vanishing of dimensions and nonexistence of spectral triples on compact Vilenkin groups

We compute the spectral dimension, the dimension of a symmetric random walk, and the Gelfand-Kirillov dimension for compact Vilenkin groups. As a result, we show that these dimensions are zero for any compact, totally disconnected, metrizable topological group. We provide an explicit description of the $K$-groups for compact Vilenkin groups. We express the generators of the $K_0$-groups in terms of the corresponding matrix coefficients for two specific examples: the group of $p$-adic integers and the $p$-adic Heisenberg group. Finally, we prove the nonexistence of a natural class of spectral triples on the group of $p$-adic integers.

math.OA↗

arXiv2025

Logarithmic correction to the entropy of a Kerr-Newman family of black holes in $U(1)^2$-charged STU supergravity models

The leading quantum-gravitational correction to the black hole entropy is known to be a universal logarithmic term. In this study, we investigate the logarithmic corrections for the black holes in the STU supergravity models, which are a bosonic truncation into a specific class of $U(1)^2$-charged Einstein-Maxwell-dilaton theory. We demonstrate how the entire Kerr-Newman-AdS and Kerr-Newman family of black holes can be recovered within the gauged and ungauged STU supergravity models as special embedding choices in 4D. Logarithmic corrections are computed using two distinct Euclidean quantum gravity setups for extremal and non-extremal limits of all embedded rotating, static, charged, and neutral black holes. Our calculations employ the on-shell heat kernel method based Seeley-DeWitt expansion computations. Notably, all the AdS$_4$ results exhibit a confirmed non-topological nature as compared to the flat counterparts, offering a natural and more comprehensive ``infrared window into the microstates'' of black holes.

hep-th↗

arXiv2024

Product of some large sets near idempotent

We characterize when the finite Cartesian product of central sets near idempotent is central near idempotent. Moreover, we provide a partial characterization for the infinite Cartesian product of the same. Then, we study the abundance of some large sets near idempotent. Also, we investigate the effect of tensor product near idempotent. Finally, as an application we provide the polynomial extension of Milliken-Taylor theorem near zero.

math.CO↗

arXiv2024

Large sets near idempotent and its product

Tootkaboni and Vahed introduced the notion of some large sets near idempotent along with some combinatorial properties. We characterize when the finite Cartesian product of central sets near idempotent is central near idempotent. Moreover, we provide a partial characterization for the infinite Cartesian product of the same. We then study the abundance of some large sets near idempotent. We also investigate the effect of tensor product near zero. Finally, as an application we provide a characterization of members of polynomials (with constant term 0) evaluated at idempotents in a near zero semigroup.

math.CO↗

arXiv2023

$W(0,b)$ algebra and the dual theory of 3D asymptotically flat higher spin gravity

BMS algebra in three spacetime dimensions can be deformed into a two parameter family of algebra known as $W(a,b)$ algebra. For $a=0$, we show that other than $W(0,-1)$, no other $W(0,b)$ algebra admits a non-degenerate bilinear and thus one can not have a Chern-Simons gauge theory formulation with them. However, they may appear in a three-dimensional gravity description, where we also need to have a spin 2 generator, that comes from the $(a=0,b=-1)$ sector. In the present work, we have demonstrated that the asymptotic symmetry algebra of a spin 3 gravity theory on flat spacetime has both the $W(0,-1)$ and $W(0,-2)$ algebras as subalgebras. We have also constructed a dual boundary field theory for this higher spin gravity theory by using the Chern-Simons/Wess-Zumino-Witten correspondence.

hep-th↗

arXiv2022

Dual Theory for maximally $\mathcal{N}$ extended flat Supergravity

Maximally $\mathcal{N}$ extended $2+1$ dimensional flat Supergravity theories exist for a class of super-Poincaré algebras for arbitrary $\mathcal{N}$. They have rich asymptotic structures and contain all interesting topological supergravity solutions in presence of non-trivial holonomy. For the asymptotic symmetry algebra being a suitable flat limit of the superconformal algebra $Osp(\mathcal{N}|2;R)$, we have found the $1+1$ dimensional chiral WZW model as the dual quantum field theory that describes the dynamics of these solutions. In the Hamiltonian analysis, the reduced phase space resembles a flat super Liouville theory.

hep-th↗

arXiv2020

D-sets in Arbitrary Semigroup

We define the notion of $D$-set in an arbitrary semigroup, and with some mild restrictions we establish its dynamical and combinatorial characterizations. Assuming a weak form of cancellation in semigroups we have shown that the Cartesian product of finitely many $D$-sets is a $D$-set. A similar partial result has been proved for Cartesian product of infinitely many $D$-sets. Finally, in a commutative semigroup we deduce that $D$-sets (with respect to a Følner net) are $C$-sets.

math.DS↗