
Author(s) 
Einsilver, Philip Schott, René 

Title  Algebraic Structures and Operators Calculus, Vol. I: Representations and Probability Theory 
Publisher  Kluwer Academic Publishers 
Year of publication  1993 
Reviewed by  VALERII V. TROFIMOV 
Lie groups and Lie algebras are not only a part of the algebra and geometry, but a common language for wide range of mathematical branches and their applications as well. The aim of the book under review is to present probability theory in connection with group representation. I think, this book corresponds undoubtedly to the unique program "Mathematics and Its Applications" (managing Editor M. Hazewinkel). From this viewpoint, the book elucidates "a central concept which plays an important role in several different mathematical and/or scientific specialization areas". With this in mind, suffice it to say that the HeisenbergWeyl algebra, Fock spaces, Riccaty equations, random walks are the fundamental notions considered here in detail.
The rough contents of the book are as follows: Introduction, 1. Introductory Noncommutative Algebra, 2. Hypergeometric functions, 3. Probability and Fock Spaces, 4. Momont Systems, 5. Bernoulli Processes, 6. Bernoulli Systems, 7. Matrix Elements.
Book has pleasant design, accessibility of the information, extensive index (327 items). The problems ending every chapters constitute important part of the book, which serves as a primary text for undergraduate students in courses on algebraic structures and operator calculus.
Purchasing of Representations and Probability Theory is a good investment for students, teachers, researchers and libraries alike.