Irreducible representations of the $C\sp{\ast} $-algebra generated by a quasinormal operator

Irreducible Representations of Operator Algebras

IRREDUCIBLE REPRESENTATIONS OF THE HAMILTONIAN ALGEBRA H(2r; n)

Let L = H(2r; n) be a graded Lie algebra of Hamiltonian type in the Cartan type series over an algebraically closed field of characteristic p > 2. In the generalized restricted Lie algebra setup, any irreducible representation of L corresponds uniquely to a (generalized) p-character χ. When the height of χ is no more than min{pni − pni−1 | i = 1, 2, . . . , 2r} − 2, the corresponding irreducibl...

CLASSIFICATION THEOREM ON IRREDUCIBLE REPRESENTATIONS OF THE q-DEFORMED ALGEBRA

The aim of this paper is to give a complete classification of irreducible finite-dimensional representations of the nonstandard q-deformation U ′ q(son) (which does not coincide with the Drinfel’d-Jimbo quantum algebra Uq(son)) of the universal enveloping algebra U(son(C)) of the Lie algebra son(C) when q is not a root of unity. These representations are exhausted by irreducible representations...

IRREDUCIBLE REPRESENTATIONS OF DEFORMED OSCILLATOR ALGEBRA AND q-SPECIAL FUNCTIONS

Different generators of a deformed oscillator algebra give rise to oneparameter families of q-exponential functions and q-Hermite polynomials related by generating functions. Connections of the Stieltjes and Hamburger classical moment problems with the corresponding resolution of unity for the q-coherent states and with ’coordinate’ operators Jacobi matrices, are also pointed out. Permanent add...

SOME QUOTIENTS ON A BCK-ALGEBRA GENERATED BY A FUZZY SET

First we show that the cosets of a fuzzy ideal μ in a BCK-algebraX form another BCK-algebra  X/μ (called the fuzzy quotient BCK-algebra of X by μ). Also we show thatX/μ is a fuzzy partition of X and we prove several some isomorphism theorems. Moreover we prove that if the associated fuzzy similarity relation of a fuzzy partition P of a commutative BCK-algebra iscompatible, then P is a fuzzy quo...