arXiv subjects

Shreema Subhash Bhatt

Publications and source records attributed to Shreema Subhash Bhatt.

3 recordsLinked to original sources

arXiv2026

$C(SO_q(4)/SO_q(2))$ as a Groupoid $C^*$-algebra

In this paper, we prove that $C(SO_q(4)/SO_q(2))$ is isomorphic to the $C^*$-algebra of the tight groupoid $\mathcal{G}_{\mathrm{tight}}$ associated with the inverse semigroup generated by the standard generators of its classical limit $C(SO_0(4)/SO_0(2))$. We show that all four orbits of the unit space $\mathcal{G}_{\mathrm{tight}}^{(0)}$ under the natural action of $\mathcal{G}_{\mathrm{tight}}$ are locally closed, and that the associated isotropy groups are isomorphic to $\mathbb{Z}$. Consequently, every irreducible representation of $C^*(\mathcal{G}_{\mathrm{tight}})$ is induced from an irreducible representation of $C^*(\mathbb{Z})$, which are parametrized by $\mathbb{T}$. In this way, we obtain four families of irreducible representations parametrized by $\mathbb{T}$, and we explicitly construct their equivalence with the corresponding Soibelman irreducible representations of $C(SO_q(4)/SO_q(2))$.

math.OA↗

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

$K$-stability of $C^*$-algebras generated by isometries and unitaries with twisted commutation relations

In this article, we prove $K$-stability for a family of $C^*$-algebras, which are generated by a finite set of unitaries and isometries satisfying twisted commutation relations. This family includes the $C^*$-algebra of doubly non-commuting isometries and free twist of isometries. Next, we consider the $C^*$-algebra $A_{\mathcal{V}}$ generated by an $n$-tuple of $\mathcal{U}$-twisted isometries $\mathcal{V}$ with respect to a fixed $n\choose 2$-tuple $\mathcal{U}=\{U_{ij}:1\leq i<j \leq n\}$ of commuting unitaries (see \cite{NarJaySur-2022aa}). Under the assumption that the spectrum of the commutative $C^*$-algebra generated by $(\{U_{ij}:1\leq i<j \leq n\})$ does not contain any element of finite order in the torus group $\bbbt^{n\choose 2}$, we show that $A_{\mathcal{V}}$ is $K$-stable. Finally, we prove the same result for the $C^*$-algebra generated by a tuple of free $\mathcal{U}$-twisted isometries.

math.OA↗