Related papers: Quantized Matrix Algebras and Quantum seeds
A concept of quantum triad and its solution is introduced. It represents a common framework for several situations where we have a quantale with a right module and a left module, provided with a bilinear inner product. Examples include Van…
We provide $\mathbb{N}$-filtrations on the negative part $U_q(\mathfrak{n}^-)$ of the quantum group associated to a finite-dimensional simple Lie algebra $\mathfrak{g}$, such that the associated graded algebra is a skew-polynomial algebra…
Quantum decision systems are being increasingly considered for use in artificial intelligence applications. Classical and quantum nodes can be distinguished based on certain correlations in their states. This paper investigates some…
Geometric quantization of a Poisson manifold need not imply quantization of its symplectic leaves. We provide the leafwise geometric quantization of a Poisson manifold, seen as a foliated one, whose quantum algebra restricted to each leaf…
Algebraic quantum field theory provides a general, mathematically precise description of the structure of quantum field theories, and then draws out consequences of this structure by means of various mathematical tools -- the theory of…
We provide a framework connecting several well known theories related to the linearity of graded modules over graded algebras. In the first part, we pay a particular attention to the tensor products of graded bimodules over graded algebras.…
The group gradings on the symmetric composition algebras over arbitrary fields are classified. Applications of this result to gradings on the exceptional simple Lie algebras are considered too.
In this paper, W*-algebras are presented as canonical colimits of diagrams of matrix algebras and completely positive maps. In other words, matrix algebras are dense in W*-algebras.
We aim to explore if inside a quantum vertex algebras, we can find the right notion of a quantum conformal algebra.
It is shown how the theory of the fields can be constructed in a consistent way in quantized spaces. All constructions are connected with unitary irreducible representations of real forms of six dimensional rotation algebras O(1,5), O(2,4),…
Positively graded algebras are fairly natural objects which are arduous to be studied. In this article we query quotients of non-standard graded polynomial rings with combinatorial and commutative algebra methods.
A way to construct and classify the three dimensional polynomially deformed algebras is given and the irreducible representations is presented. for the quadratic algebras 4 different algebras are obtained and for cubic algebras 12 different…
Quantum algorithm is an algorithm for solving mathematical problems using quantum systems encoded as information, which is found to outperform classical algorithms in some specific cases. The objective of this study is to develop a quantum…
We show how to construct the exact factorized S-matrices of 1+1 dimensional quantum field theories whose symmetry charges generate a quantum affine algebra. Quantum affine Toda theories are examples of such theories. We take into account…
Cluster algebras have recently become an important player in mathematics and physics. In this work, we investigate them through the lens of modern data science, specifically with techniques from network science and machine learning. Network…
We consider integrable vertex models whose Boltzmann weights (R-matrices) are trigonometric solutions to the graded Yang-Baxter equation. As is well known the latter can be generically constructed from quantum affine superalgebras…
We produce graded monoidal categorifications of the quantum boson algebras in any symmetrizable Kac-Moody type. Our categories are defined in terms of diagrammatic generators and relations and have a faithful 2-representation on…
We investigate invertible matrices over finite additively idempotent semirings. The main result provides a criterion for the invertibility of such matrices. We also give a construction of the inverse matrix and a formula for the number of…
We present two complementary ways in which Saraceno's symmetric version of the quantum baker's map can be written as a shift map on a string of quantum bits. One of these representations leads naturally to a family of quantizations of the…
The quantum symmetry of a rational quantum field theory is a finite- dimensional multi-matrix algebra. Its representation category, which determines the fusion rules and braid group representations of superselection sectors, is a braided…