相关论文: Projective modules over the fuzzy four-sphere
The q-deformed fuzzy Dirac and chirality operators on quantum fuzzy four-sphere $ S^{4}_{qF} $. Using the q-deformed fuzzy Ginsparg-Wilson algebra, it has been studied the q-deformed fuzzy Dirac and chirality operators in instanton and…
We present a method for building physical projector operators for multi-leg helicity amplitudes. For any helicity configuration of the external particles, we define a physical projector which singles out the corresponding helicity…
Equivariance under the action of Uq(so(5)) is used to compute the left regular and (chiral) spinorial representations of the algebra of the orthogonal quantum 4-sphere S^4_q. These representations are the constituents of a spectral triple…
We study a noncommutative gauge theory on a fuzzy four-sphere. The idea is to use a matrix model with a fifth-rank Chern-Simons term and to expand matrices around the fuzzy four-sphere which corresponds to a classical solution of this…
When considered as submanifolds of Euclidean space, the Riemannian geometry of the round sphere and the Clifford torus may be formulated in terms of Poisson algebraic expressions involving the embedding coordinates, and a central object is…
We give a construction of the monopole bundles over fuzzy complex projective spaces as projective modules. The corresponding Chern classes are calculated. They reduce to the monopole charges in the N -> infinity limit, where N labels the…
We generalise the construction of fuzzy CP^N in a manner that allows us to access all noncommutative equivariant complex vector bundles over this space. We give a simplified construction of polarization tensors on S^2 that generalizes to…
In this paper we study Rota-Baxter modules with emphasis on the role played by the Rota-Baxter operators and resulting difference between Rota-Baxter modules and the usual modules over an algebra. We introduce the concepts of free,…
We study polynomial deformations of the fuzzy sphere, specifically given by the cubic or the Higgs algebra. We derive the Higgs algebra by quantizing the Poisson structure on a surface in $\mathbb{R}^3$. We find that several surfaces,…
A fuzzy circle and a fuzzy 3-sphere are constructed as subspaces of fuzzy complex projective spaces, of complex dimension one and three, by modifying the Laplacians on the latter so as to give unwanted states large eigenvalues. This leaves…
Generalizing differential geometry of smooth vector bundles formulated in algebraic terms of the ring of smooth functions, its derivations and the Koszul connection, one can define differential operators, differential calculus and…
I carefully study noncommutative version of ADHM construction of instantons, which was proposed by Nekrasov and Schwarz. Noncommutative ${\bf R}^4$ is described as algebra of operators acting in Fock space. In ADHM construction of…
We construct representations of a q-oscillator algebra by operators on Fock space on positive matrices. They emerge from a multiresolution scaling construction used in wavelet analysis. The representations of the Cuntz Algebra arising from…
In this paper, we explicitly construct a series of projectors on integral noncommutative orbifold $T^2/Z_4$ by extended $GHS$ constrution. They include integration of two arbitary functions with $Z_4$ symmetry. Our expressions possess…
We use operator algebras and operator theory to obtain new result concerning Berezin quantization of compact K\"ahler manifolds. Our main tool is the notion of subproduct systems of finite-dimensional Hilbert spaces, which enables all…
In this note we give an explicit description of the irreducible components of the reduced point varieties of quantum polynomial algebras.
A new explicitly correlated functional form for expanding the wave function of an N-particle system with arbitrary angular momentum and parity is presented. We develop the projection-based approach, numerically exploited in our previous…
A classical result asserts that the complex projective plane modulo complex conjugation is the 4-dimensional sphere. We generalize this result in two directions by considering the projective planes over the normed real division algebras and…
In this paper, we set up the bi-module of the algebra ${\cal A}$ on fuzzy sphere. Based on the differential operators in moving frame, we generalize the ABS construction into fuzzy sphere case. The applications of ABS construction are…
In this article, we introduce and study the concept of $\textit{spherical-vectors}$, which can be perceived as a natural extension of the arguments of complex numbers in the context of quaternions. We initially establish foundational…