Related papers: SU(2) Action-Angle Variables

We present two classes of examples of Hopf algebroids associated with noncommutative principal bundles. The first comes from deforming the principal bundle while leaving unchanged the structure Hopf algebra. The second is related to…

We consider a q-analogue of the standard bilinear form on the commutative ring of symmetric functions. The q=-1 case leads to a Z-graded Hopf superalgebra which we call the algebra of odd symmetric functions. In the odd setting we describe…

We describe an application of the linear $\de$-expansion to the calculation of correlation functions in SU(2)-Higgs lattice gauge theory. A significant advantage of the technique is that an infinite volume lattice may be used, allowing the…

We here present rudiments of an approach to geometric actions in noncommutative algebraic geometry, based on geometrically admissible actions of monoidal categories. This generalizes the usual (co)module algebras over Hopf algebras which…

We give a detailed description of the resolution of the identity of a second order $q$-difference operator considered as an unbounded self-adjoint operator on two different Hilbert spaces. The $q$-difference operator and the two choices of…

Action of finite-dimensional Hopf algebra $H$ on commutative $k-$algebra $A$ is considered. As a generalization of the well-known fact for finite groups S. Montgomery raised a problem in 1993 whether $A$ is integral over subalgebra of…

We know definition of Rota--Baxter operators on different algebraic systems. For examples, on groups, on algebras, on Hopf algebras. On some algebraic systems it is possible to define different types of Rota--Baxter operators. For example,…

An AF-algebra is assigned to each cusp form f of weight two; we study properties of this operator algebra, when f is a Hecke eigenform.

We consider a second order self-adjoint operator in a domain which can be bounded or unbounded. The boundary is partitioned into two parts with Dirichlet boundary condition on one of them, and Neumann condition on the other. We assume that…

Let H be a semisimple (so, finite dimensional) Hopf algebra over an algebraically closed field k of characteristic zero and let A be a commutative domain over k. We show that if A arises as an H-module algebra via an inner faithful…

The matrix elements connected non physic angles space representation with the space of physic observables of alternative O(2,4) world found on explicit form. All such matrix elements are represented in terms of solutions of Gauss…

In this paper a finite dimensional unital associative algebra is presented, and its group of algebra automorphisms is detailed. The studied algebra can physically be understood as the creation operator algebra in a formal quantum field…

We construct a class of non-commutative, non-cocommutative, semisimple Hopf algebras of dimension $2n^2$ and present conditions to define an inner faithful action of these Hopf algebras on quantum polynomial algebras, providing, in this…

A method is discussed to analyze the dynamics of a dissipative quantum system. The method hinges upon the definition of an alternative (time-dependent) product among the observables of the system. In the long time limit this yields a…

Non-commutative Quantum Mechanics in 3D is investigated in the framework of the abelian Drinfeld twist which deforms a given Hopf algebra while preserving its Hopf algebra structure. Composite operators (of coordinates and momenta) entering…

We consider systems where dynamical variables are the generators of the SU(2) group. A subset of these Hamiltonians is exactly solvable using the Bethe ansatz techniques. We show that Bethe ansatz equations are equivalent to polynomial…

Let F be a real quadratic field with ring of integers O and with class number 1. Let Gamma be a congruence subgroup of GL_2 (O). We describe a technique to compute the action of the Hecke operators on the cohomology H^3 (Gamma; C). For F…

We formulate the $O(3) \s-$ model on fuzzy sphere and construct the Hopf term. We show that the field can be expanded in terms of the ladder operators of Holstein-Primakoff realisation of SU(2) algebra and the corresponding basis set can be…

Ladder operators are useful, if not essential, in the analysis of some given physical system since they can be used to find easily eigenvalues and eigenvectors of its Hamiltonian. In this paper we extend our previous results on abstract…

The properties of Hopf star operations and twisted Hopf stars operations on quantum groups are discussed in relation with the theory of representations (star representations). Invariant Hermitian sesquilinear forms (scalar products) on…