Non-commutative probability and non-commutative processes: Beyond the Heisenberg algebra

Non-commutative combinatorial algebra

Acceptable random variables in non-commutative probability spaces

Acceptable random variables are defined in noncommutative (quantum) probability spaces and some of probability inequalities for these classes  are obtained. These results are a generalization of negatively orthant dependent random variables in probability theory. Furthermore, the obtained results can be used for random matrices.

Non-commutative Hopf algebra of formal diffeomorphisms

The subject of this paper are two Hopf algebras which are the non-commutative analogues of two different groups of formal power series. The first group is the set of invertible series with the group law being multiplication of series, while the second group is the set of formal diffeomorphisms with the group law being composition of series. The motivation to introduce these Hopf algebras comes ...

Non-commutative oscillators and the commutative limit

It is shown in first order perturbation theory that anharmonic oscillators in non-commutative space behave smoothly in the commutative limit just as harmonic oscillators do. The non-commutativity provides a method for converting a problem in degenerate perturbation theory to a non-degenerate problem. In the last few years theories in non-commutative space [1]-[5] have been studied extensively. ...

Commutative Algebra Commutative Algebra : General