Representations of the (infinite) canonical anticommutation relations and the associated operator algebra, the fermion algebra, are studied. A "coupling constant" (in (0,1]) is defined for primary states of "finite type" of that algebra. Primary, faithful states of finite type with arbitrary coupling are constructed and classified. Their physical significance for quantum thermodynamical systems...

We construct a universal tangle invariant on a quantum algebra. We show that the invariant maps tangle to commutants of the algebra; every (1, 1)-tangle is mapped to a Casimir operator of the algebra; the eigenvalue of the Casimir operator in an irreducible representation of the algebra is a link polynomial for the closure of the tangle. This result is applied to a discussion of the Alexander–C...

This paper is an exposition of the representation theory of vertex operator algebras in terms of associative algebras An(V ) and their bimodules. A new result on the rationality is given. That is, a simple vertex operator algebra V is rational if and only if its Zhu algebra A(V ) is a semisimple associative algebra. 2000MSC:17B69

The main result of this report is that every demonic refinement algebra with enabledness and termination is isomorphic to an algebra of ordered pairs of elements of a Kleene algebra with domain and with a divergence operator satisfying a mild condition. Divergence is an operator producing a test interpreted as the set of states from which nontermination may occur.

We prove a quantized version of a theorem by M. V. Shĕınberg: A uniform algebra equipped with its canonical, i.e. minimal, operator space structure is operator amenable if and only if it is a commutative C∗-algebra.

We present a vertex operator algebra which is an extension of the level k vertex operator algebra for the ŝl2 conformal field theory. We construct monomial basis of its irreducible representations.

The diagonalization of the Heun–Racah operator is studied with help modified algebraic Bethe ansatz. This most general bilinear expression in two generators Racah algebra. A presentation this algebra given terms dynamical operators and allows construction vectors for operator. associated equations are derived both homogeneous inhomogeneous cases.

We find a Jacobi identity for intertwining operator algebras. Most of the main properties of genus-zero conformal field theories, including the main properties of vertex operator algebras, modules, intertwining operators, Verlinde algebras, and fusing and braiding matrices, are incorporated into this identity. We prove that intertwining operators for a suitable vertex operator algebra satisfy t...