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Noetherian Semigroup Algebras: Algebra and Applications, cartea 7

Autor Eric Jespers, Jan Okninski
en Limba Engleză Paperback – 16 noi 2010
The ?rst aim of this work is to present the main results and methods of the theory of Noetherian semigroup algebras. These general results are then applied and illustrated in the context of certain interesting and important concrete classes of algebras that arise in a variety of areas and have been recently intensively studied. One of the main motivations for this project has been the growing int- est in the class of semigroup algebras (and their deformations) and in the application of semigroup theoretical methods. Two factors seem to be the cause for this. First, this ?eld covers several important classes of algebras that recently arise in a variety of areas. Furthermore, it provides methods to construct a variety of examples and tools to control their structure and properties, that should be of interest to a broad audience in algebra and its applications. Namely, this is a rich resource of constructions not only for the noncommutative ring theorists (and not only restricted to Noetherian rings) but also to researchers in semigroup theory and certain aspects of group theory. Moreover, because of the role of new classes of Noetherian algebras in the algebraic approach in noncommutative geometry, algebras of low dimension (in terms of the homological or the Gelfand-Kirillov - mension) recently gained a lot of attention. Via the applications to the Yang-Baxter equation, the interest also widens into other ?elds, most - tably into mathematical physics.
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Specificații

ISBN-13: 9789048174485
ISBN-10: 9048174481
Pagini: 376
Ilustrații: X, 364 p.
Dimensiuni: 155 x 235 x 20 mm
Greutate: 0.53 kg
Ediția:Softcover reprint of hardcover 1st ed. 2007
Editura: SPRINGER NETHERLANDS
Colecția Springer
Seria Algebra and Applications

Locul publicării:Dordrecht, Netherlands

Public țintă

Research

Cuprins

Prerequisites on semigroup theory.- Prerequisites on ring theory.- Algebras of submonoids of polycyclic-by-finite groups.- General Noetherian semigroup algebras.- Principal ideal rings.- Maximal orders and Noetherian semigroup algebras.- Monoids of I-type.- Monoids of skew type.- Examples.

Recenzii

From the reviews:
"This book presents the main results and methods of the theory of Noetherian semigroup algebras over fields. … This is a highly technical and specialized monograph that will primarily be of use to researchers in the theory of semigroup algebras … . The many examples given in detail, and the general theory developed, may prove useful to those working in ring or semigroup theory." (Henry E. Heatherly, Mathematical Reviews, Issue 2007 k)
"This work presents a comprehensive treatment of the main results and methods of the theory of Noetherian semigroup algebras. … The main subject in this book is to present when some semigroup algebras are Noetherian and how they are under the Noetherian condition. … This book is a good reference for researchers who are interested in non-commutative algebra and non-commutative geometry through the method of semigroups." (Li Fang, Zentralblatt MATH, Vol. 1135 (13), 2008)
"The book under review is testament to the huge amount and the depth of research on Noetherian semigroup algebras. … The authors have brought together work from a significant number of research papers and made a coherent whole. … it is definitely the place to learn about Noetherian semigroup algebras. Essential reading for people interested in semigroup algebras, it will also be of interest to semigroup theorists, particularly because of the wealth of new examples of semigroups it provides." (John Fountain, Semigroup Forum, Vol. 79, 2009)

Textul de pe ultima copertă

Within the last decade, semigroup theoretical methods have occurred naturally in many aspects of ring theory, algebraic combinatorics, representation theory and their applications. In particular, motivated by noncommutative geometry and the theory of quantum groups, there is a growing interest in the class of semigroup algebras and their deformations.
This work presents a comprehensive treatment of the main results and methods of the theory of Noetherian semigroup algebras. These general results are then applied and illustrated in the context of important classes of algebras that arise in a variety of areas and have been recently intensively studied. Several concrete constructions are described in full detail, in particular intriguing classes of quadratic algebras and algebras related to group rings of polycyclic-by-finite groups. These give new classes of Noetherian algebras of small Gelfand-Kirillov dimension. The focus is on the interplay between their combinatorics and the algebraic structure. This yields a rich resource of examples that are of interest not only for the noncommutative ring theorists, but also for researchers in semigroup theory and certain aspects of group and group ring theory. Mathematical physicists will find this work of interest owing to the attention given to applications to the Yang-Baxter equation.

Caracteristici

Offers a comprehensive treatment of the current state of a fast-developing area of noncommutative algebra Provides a significant source of concrete constructions in noncommutative (noetherian) ring theory, semigroup theory and group theory; carefully discusses numerous examples Exhibits strong links between the structure and combinatorics of algebras Explores connections and applications to wider areas of current research, most notably theory of growth of algebras and aspects of mathematical physics