A. Kuzmin

activity

20172024

most citedOn

q

-tensor product of Cuntz algebras

3 citations · 3 across the 7 of their papers we have counts for

collaborators

7 papers

math.OA2024

Universal C*-algebras generated by doubly non-commuting isometries

Marcel de Jeu, Alexey Kuzmin, Paulo R. Pinto

We give an explicit injective representation of the universal $C^{*}$ -algebra that is generated by doubly non-commuting isometries. This injectivity allows us to prove th…

math.OA2022

CCR and CAR algebras are connected via a path of Cuntz-Toeplitz algebras

Alexey Kuzmin

For $q \in R$ , $∣ q ∣ < 1$ we consider the universal enveloping $C^{*}$ -algebra of a $*$ -algebra of $q$ -canonical commutation relations ( $q$ -CCR), which is generated by $a_1,…

math.DG2022

Index theory of hypoelliptic operators on Carnot manifolds

Magnus Goffeng, Alexey Kuzmin

We study the index theory of hypoelliptic operators on Carnot manifolds -- manifolds whose Lie algebra of vector fields is equipped with a filtration induced from sub-bundles of th…

math.OA2021

On $q$ -tensor products of Cuntz algebras

Alexey Kuzmin, Vasyl Ostrovskyi, Danylo Proskurin +2

We consider the $C^{*}$ -algebra $E_{n, m}^{q}$ , which is a $q$ -twist of two Cuntz-Toeplitz algebras. For the case $∣ q ∣ < 1$ , we give an explicit formula which untwists the $q$ -d…

math.OA2020

Classification of irrational $Θ$ -deformed CAR $C^{*}$ -algebras

Alexey Kuzmin, Lyudmila Turowska

Given a skew-symmetric real $n \times n$ matrix $Θ$ we consider the universal enveloping $C^{*}$ -algebra $CAR_{Θ}$ of the $*$ -algebra generated by $a_{1}, \dots, a_{n}$ subject to…

math.OA2019★ 3 cited

On $q$ -tensor product of Cuntz algebras

Alexey Kuzmin, Vasyl Ostrovskyi, Danylo Proskurin +1

We consider $C^{*}$ -algebra $E_{n, m}^{q}$ , which is a $q$ -twist of two Cuntz-Toeplitz algebras. For the case $∣ q ∣ < 1$ we give an explicit formula, which untwists the $q$ -defor…

math.QA2017

Faithfulness of the Fock representation of $C^{*}$ -algebra generated by $q_{ij}$ -commuting isometries

Alexey Kuzmin, Nikolay Pochekai

We consider $C^{*}$ -algebra $I so m_{q_{ij}}$ generated by $n$ isometries $a_{1}, \dots, a_{n}$ satisfying the relations $a_{i}^{*} a_{j} = q_{ij} a_{j} a_{i}^{*}$ with $max ∣ q_{ij} ∣ < 1$ . This $C^*…

Universal C*-algebras generated by doubly non-commuting isometries

CCR and CAR algebras are connected via a path of Cuntz-Toeplitz algebras

Index theory of hypoelliptic operators on Carnot manifolds

On q-tensor products of Cuntz algebras

Classification of irrational Θ-deformed CAR C∗-algebras

On q-tensor product of Cuntz algebras

Faithfulness of the Fock representation of C∗-algebra generated by qij​-commuting isometries

On $q$ -tensor products of Cuntz algebras

Classification of irrational $Θ$ -deformed CAR $C^{*}$ -algebras

On $q$ -tensor product of Cuntz algebras

Faithfulness of the Fock representation of $C^{*}$ -algebra generated by $q_{ij}$ -commuting isometries