This book gives a state of the art approach to the study of
polynomial identities satisfied by a given algebra by combining
methods of ring theory, combinatorics, and representation theory of
groups with analysis. The idea of applying analytical methods to
the theory of polynomial identities appeared in the early 1970s and
this approach has become one of the most powerful tools of the
theory. A PI-algebra is any algebra satisfying at least one
nontrivial polynomial identity.This includes the polynomial rings
in one or several variables, the Grassmann algebra,
finite-dimensional algebras, and many other algebras occurring
naturally in mathematics. The core of the book is the proof that
the sequence of co dimensions of any PI-algebra has integral
exponential growth - the PI-exponent of the algebra. Later chapters
further apply these results to subjects such as a characterization
of varieties of algebras having polynomial growth and a
classification of varieties that are minimal for a given exponent.
Results are extended to graded algebras and algebras with
involution. The book concludes with a study of the numerical
invariants and their asymptotics in the class of Lie algebras. Even
in algebras that are close to being associative, the behavior of
the sequences of co dimensions can be wild. The material is
suitable for graduate students and research mathematicians
interested in polynomial identity algebras.
General
Imprint: |
American Mathematical Society
|
Country of origin: |
United States |
Series: |
Mathematical Surveys and Monographs |
Release date: |
November 2005 |
Authors: |
Antonio Giambruno
• Mikhail Zaicev
|
Format: |
Hardcover
|
Pages: |
352 |
Edition: |
illustrated Edition |
ISBN-13: |
978-0-8218-3829-7 |
Categories: |
Books
|
LSN: |
0-8218-3829-6 |
Barcode: |
9780821838297 |
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