Download or read book Trace Rings of Generic 2 by 2 Matrices written by Lieven Le Bruyn and published by American Mathematical Soc.. This book was released on 1987 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we study the trace ring of [italic]m generic 2 by 2 matrices [capital Greek]Pi[italic subscript]m,2. It is shown that it is a polynomial ring over the generic Clifford algebra for [italic]m-ary quadratic forms of rank [less than or equal to] 3. We prove that it is a Cohen-Macaulay module, i.e. it is a free module of finite rank over a polynomial subring of the center. This explains the existence of a functional equation for its Poincaré series.
Download or read book Trace Rings of Generic 2 by 2 Matrices written by Lieven Le Bruyn and published by . This book was released on 1987 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Polynomial Identity Rings written by Vesselin Drensky and published by Birkhäuser. This book was released on 2012-12-06 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lecture notes treat polynomial identity rings from both the combinatorial and structural points of view. The greater part of recent research in polynomial identity rings is about combinatorial questions, and the combinatorial part of the lecture notes gives an up-to-date account of recent research. On the other hand, the main structural results have been known for some time, and the emphasis there is on a presentation accessible to newcomers to the subject.
Download or read book The Polynomial Identities and Invariants of n times n Matrices written by Edward Formanek and published by American Mathematical Soc.. This book was released on 1991 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of polynomial identities, as a well-defined field of study, began with a well-known 1948 article of Kaplansky. The field has since developed along two branches: the structural, which investigates the properties of rings which satisfy a polynomial identity; and the varietal, which investigates the set of polynomials in the free ring which vanish under all specializations in a given ring. This book is based on lectures delivered during an NSF-CBMS Regional Conference, held at DePaul University in July 1990, at which the author was the principal lecturer. The first part of the book is concerned with polynomial identity rings. The emphasis is on those parts of the theory related to n x n matrices, including the major structure theorems and the construction of certain polynomials identities and central polynomials for n x n matrices. The ring of generic matrices and its centre is described. The author then moves on to the invariants of n x n matrices, beginning with the first and second fundamental theorems, which are used to describe the polynomial identities satisfied by n x n matrices. One of the exceptional features of this book is the way it emphasizes the connection between polynomial identities and invariants of n x n matrices. Accessible to those with background at the level of a first-year graduate course in algebra, this book gives readers an understanding of polynomial identity rings and invariant theory, as well as an indication of current problems and research in these areas.
Download or read book Rings with Polynomial Identities and Finite Dimensional Representations of Algebras written by Eli Aljadeff and published by American Mathematical Soc.. This book was released on 2020-12-14 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: A polynomial identity for an algebra (or a ring) A A is a polynomial in noncommutative variables that vanishes under any evaluation in A A. An algebra satisfying a nontrivial polynomial identity is called a PI algebra, and this is the main object of study in this book, which can be used by graduate students and researchers alike. The book is divided into four parts. Part 1 contains foundational material on representation theory and noncommutative algebra. In addition to setting the stage for the rest of the book, this part can be used for an introductory course in noncommutative algebra. An expert reader may use Part 1 as reference and start with the main topics in the remaining parts. Part 2 discusses the combinatorial aspects of the theory, the growth theorem, and Shirshov's bases. Here methods of representation theory of the symmetric group play a major role. Part 3 contains the main body of structure theorems for PI algebras, theorems of Kaplansky and Posner, the theory of central polynomials, M. Artin's theorem on Azumaya algebras, and the geometric part on the variety of semisimple representations, including the foundations of the theory of Cayley–Hamilton algebras. Part 4 is devoted first to the proof of the theorem of Razmyslov, Kemer, and Braun on the nilpotency of the nil radical for finitely generated PI algebras over Noetherian rings, then to the theory of Kemer and the Specht problem. Finally, the authors discuss PI exponent and codimension growth. This part uses some nontrivial analytic tools coming from probability theory. The appendix presents the counterexamples of Golod and Shafarevich to the Burnside problem.
Download or read book Invariant Theory written by Sebastian S. Koh and published by Springer. This book was released on 2006-11-15 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of expository papers is the outgrowth of a conference in combinatorics and invariant theory. In recent years, newly developed techniques from algebraic geometry and combinatorics have been applied with great success to some of the outstanding problems of invariant theory, moving it back to the forefront of mathematical research once again. This collection of papers centers on constructive aspects of invariant theory and opens with an introduction to the subject by F. Grosshans. Its purpose is to make the current research more accesssible to mathematicians in related fields.
Download or read book Algebraic Groups Utrecht 1986 written by Arjeh M. Cohen and published by Springer. This book was released on 2006-11-15 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: From 1-4 April 1986 a Symposium on Algebraic Groups was held at the University of Utrecht, The Netherlands, in celebration of the 350th birthday of the University and the 60th of T.A. Springer. Recognized leaders in the field of algebraic groups and related areas gave lectures which covered wide and central areas of mathematics. Though the fourteen papers in this volume are mostly original research contributions, some survey articles are included. Centering on the Symposium subject, such diverse topics are covered as Discrete Subgroups of Lie Groups, Invariant Theory, D-modules, Lie Algebras, Special Functions, Group Actions on Varieties.
Download or read book Graded Orders written by F.M., van Oystaeyen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a clear, well-developed presentation this book provides the first systematic treatment of structure results for algebras which are graded by a goup. The fruitful method of constructing graded orders of special kind over a given order, culminating in applications of the construction of generalized Rees rings associated to divisors, is combined with the theory of orders over graded Krull domains. This yields the construction of generalized Rees rings corresponding to the central ramification divisor of the orders and the algebraic properties of the constructed orders. The graded methods allow the study of regularity conditions on order. The book also touches upon representation theoretic methods, including orders of finite representation type and other aspects of this theory applicable to the classification of orders. The final chapter describes the ring theoretical approach to the classification of orders of global dimension two, originally carried out by M. Artin using more geometrical methods. Since its subject is important in many research areas, this book will be valuable reading for all researchers and graduate students with an interest in non-commutative algebra.
Download or read book Noncommutative Geometry and Cayley smooth Orders written by Lieven Le Bruyn and published by CRC Press. This book was released on 2007-08-24 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noncommutative Geometry and Cayley-smooth Orders explains the theory of Cayley-smooth orders in central simple algebras over function fields of varieties. In particular, the book describes the etale local structure of such orders as well as their central singularities and finite dimensional representations. After an introduction to partial d
Download or read book Ring Theory V2 written by and published by Academic Press. This book was released on 1988-07-01 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ring Theory V2
Download or read book S minaire d Alg bre Paul Dubreil et Marie Paul Malliavin written by Marie-Paule Malliavin and published by Springer. This book was released on 2006-12-08 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Handbook of Algebra written by M. Hazewinkel and published by Elsevier. This book was released on 2000-04-06 with total page 899 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Algebra
Download or read book Noise Oscillators and Algebraic Randomness written by Michel Planat and published by Springer. This book was released on 2008-01-11 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noise is ubiquitous in nature and in man-made systems. Noise in oscillators perturbs high-technology devices such as time standards or digital communication systems. The understanding of its algebraic structure is thus of vital importance. The book addresses both the measurement methods and the understanding of quantum, 1/f and phase noise in systems such as electronic amplifiers, oscillators and receivers, trapped ions, cosmic ray showers and in commercial applications. A strong link between 1/f noise and number theory is emphasized. The twenty papers in the book are comprehensive versions of talks presented at a school in Chapelle des Bois (Jura, France) held from April 6 to 10, 1999, by engineers, physisicts and mathematicians.
Download or read book Trends in Ring Theory written by Vlastimil Dlab and published by American Mathematical Soc.. This book was released on 1998 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Ring Theory Conference, held a the University of Miskolc, Hungary, successfully accomplished its two goals: to reflect contemporary trends in the subject area; and to offer a meeting place for a large number of Eastern European algebraists and their colleagues from around the world. Particular emphasis was placed on recent developments in the following four areas: representation theory, group algebras, PI algebras and general ring theory. This book presents 13 of the invited lectures.
Download or read book Perspectives in Ring Theory written by Freddy Van Oystaeyen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings is composed of the papers resulting from the NATO work-shop "Perspectives in Ring Theory" and the work-shop "Geometry and Invariant The ory of Representations of Quivers" . Three reports on problem sessions have been induced in the part corresponding to the work-shop where they belonged. One more report on a problem session, the "lost" problem session, will be published elsewhere eventually. vii Acknowledgement The meeting became possible by the financial support of the Scientific Affairs Division of NATO. The people at this division have been very helpful in the orga nization of the meeting, in particular we commemorate Dr. Mario di Lullo, who died unexpectedly last year, but who has been very helpful with the organization of earlier meetings in Ring Theory. For additional financial support we thank the national foundation for scientific research (NFWO), the rector of the University of Antwerp, UIA, and the Belgian Ministry of Education. We also gladly acknowledge support from the Belgian Friends of the Hebrew University and the chairman Prof. P. Van Remoortere who honored Prof. S. Amitsur for his continuous contributions to the mathematical activities at the University of Antwerp. I thank the authors who contributed their paper(s) to this proceedings and the lecturers for their undisposable contributions towards the success of the work-shop. Finally I thank Danielle for allowing me to spoil another holiday period in favor of a congress.
Download or read book The Trace Ring of 2 Generic 3x3 matrices is Not Regular written by Lieven Le Bruyn and published by . This book was released on 1984 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hopf Algebras and Quantum Groups written by Stefaan Caenepeel and published by CRC Press. This book was released on 2019-05-07 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is based on the proceedings of the Hopf-Algebras and Quantum Groups conference at the Free University of Brussels, Belgium. It presents state-of-the-art papers - selected from over 65 participants representing nearly 20 countries and more than 45 lectures - on the theory of Hopf algebras, including multiplier Hopf algebras and quantum g
