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Local derivations of quantum plane algebra
Communications in Algebra, 2023– Let k be a field and q∈k* not a root of unity. We prove that on the quantum plane algebra Pq(k)=kq[x,y] any local derivation is a derivation.
A. Louly
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Quantization of the derivation Lie algebra over quantum torus
Communications in Algebra, 2023Recently, Lie bialgebra structures of the derivation Lie algebra over quantum torus were determined. In this paper, we use the general method of quantization by a Drinfel’d twist to quantize these algebras with their Lie bialgebra structures and present ...
Shuoyang Xu, Xiaoqing Yue
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BV Structure on Hochschild Cohomology of Quantum Exterior Algebra with Two Variables
Algebra Colloquium, 2023Let [Formula: see text] over a field [Formula: see text]. We give a clear characterization of the Batalin-Vilkovisky algebraic structure on Hochschild cohomology of [Formula: see text] for any [Formula: see text], and the Gerstenhaber algebraic structure
B. Hou, Jinzhong Wu
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Quantum Register Algebra: the mathematical language for quantum computing
Quantum Information Processing, 2022We present Quantum Register Algebra (QRA) as an efficient tool for quantum computing. We show the direct link between QRA and Dirac formalism. We present Geometric Algebra Algorithms Optimizer (GAALOP) implementation of our approach.
J. Hrdina +7 more
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Quantum Information Processing, 2021
We consider a quantum probe P undergoing pure dephasing due to its interaction with a quantum system S. The dynamics of P is then described by a well-defined sub-algebra of operators of S, i.e.
Fattah Sakuldee, Ł. Cywiński
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We consider a quantum probe P undergoing pure dephasing due to its interaction with a quantum system S. The dynamics of P is then described by a well-defined sub-algebra of operators of S, i.e.
Fattah Sakuldee, Ł. Cywiński
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𝑞-Tricomi functions and quantum algebra representations
Georgian Mathematical Journal, 2020The quantum groups nowadays attract a considerable interest of mathematicians and physicists. The theory of q-special functions has received a group-theoretic interpretation using the techniques of quantum groups and quantum algebras.
M. Riyasat, Tabinda Nahid, Subuhi Khan
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Quantum-mechanical correlations and Tsirelson bound from geometric algebra
Quantum Studies: Mathematics and Foundations, 2020The Bell–Clauser–Horne–Shimony–Holt inequality can be used to show that no local hidden-variable theory can reproduce the correlations predicted by quantum mechanics (QM). It can be proved that certain QM correlations lead to a violation of the classical
Carsten Held
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RLL-Realization of two-parameter quantum affine algebra in type Cn(1)
Journal of Algebra and its ApplicationsWe establish an explicit correspondence between the Drinfeld current algebra presentation for the two-parameter quantum affine algebra $U_{r, s}(\mathrm{C}_n^{(1)})$ and the $R$-matrix realization \'a la Faddeev, Reshetikhin and Takhtajan.
Xin Zhong, Naihong Hu, Naihuan Jing
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Vertex representation of quantum N-toroidal algebra for type F4
Communications in Algebra, 2020Recently Gao-Jing-Xia-Zhang defined the structures of quantum N-toroidal algebras uniformally, which are a kind of natural generalizations of the classical quantum toroidal algebras, just like the relation between 2-toroidal Lie algebras and N-toroidal ...
Cenlei Ying, L. Xia, Honglian Zhang
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Quantum Algebra Symmetry of the ASEP with Second-Class Particles
, 2015We consider a two-component asymmetric simple exclusion process (ASEP) on a finite lattice with reflecting boundary conditions. For this process, which is equivalent to the ASEP with second-class particles, we construct the representation matrices of the
V. Belitsky, G. M. Schütz
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