Generalized standard algebras

Standard Generalized Vectors for Partial O*-algebras

Standard generalized vectors for an O*-algebra N lead to a Tomita-Takesaki theory of modular automorphisms on N, and this is a key step in constructing KMS states on N (which would represent equilibrium states if N is the observable algebra of some physical system). In this paper, we extend to partial O*-algebras the notion of standard generalized vector and we show that they indeed satisfy the...

Affine Hecke algebras and generalized standard Young tableaux

This paper introduces calibrated representations for affine Hecke algebras and classifies and constructs all finite-dimensional irreducible calibrated representations. The primary technique is to provide indexing sets for controlling the weight space structure of finite-dimensional modules for the affine Hecke algebra. Using these indexing sets we show that (1) irreducible calibrated representa...

Generalized Witt Algebras and Generalized Poisson Algebras

It is well known that the Poisson Lie algebra is isomorphic to the Hamiltonian Lie algebra [1],[3],[13]. We show that the Poisson Lie algebra can be embedded properly in the special type Lie algebra [13]. We also generalize the Hamitonian Lie algebra using exponential functions, and we show that these Lie algebras are simple.

Multiplicative bijective maps on standard operator algebras

Generalized states on EQ-algebras

In this paper, we introduce a notion of generalized states from an EQ-algebra E1 to another EQ-algebra E2, which is a generalization of internal states (or state operators) on an EQ-algebra E. Also we give a type of special generalized state from an EQ-algebra E1 to E1, called generalized internal states (or GI-state). Then we give some examples and basic properties of generalized (internal) st...