Commuting Elements in Q-Deformed Heisenberg Algebras

Information theory was developed during the last decades within electrical communications, but it is almost unknown in physics. The closest approach to information theory in physics is the "calculus of propositions", which has been used in books on the frontier of quantum mechanics and the general theory of relativity. A discussion of the principles of information theory required in this book is given in Chapter 2. The ability to think readily in terms of a finite number of discrete samples is developed over many years of using information theory and digital computers, just as the ability to think readily in terms of a continuum is developed by long use of differential calculus Immediate consequences of the commutation relations; bases and normal form in H(q) and H(q,J); degree in and gradation of H(q,J); centralisers of elements in H(q,J); centralisers of elements in H(q); algebraic dependence of commuting elements in H(q) and H(q,J); representations of H(q,J) by q-difference operators; the diamond lemma; degree functions and gradations; q-special combinatorics