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Dimensions And Cast Algebras
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Book Synopsis Dimensions and $C^\ast $-Algebras by : Edward G. Effros
Download or read book Dimensions and $C^\ast $-Algebras written by Edward G. Effros and published by American Mathematical Soc.. This book was released on 1981 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discusses elementary algebras and $C DEGREES*$-algebras, namely those which are direct limits of complex semi simple al
Book Synopsis Finite Dimensional Algebras and Related Topics by : V. Dlab
Download or read book Finite Dimensional Algebras and Related Topics written by V. Dlab and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on invited lectures at the 1992 Canadian Algebra Seminar, this volume represents an up-to-date and unique report on finite-dimensional algebras as a subject with many serious interactions with other mathematical disciplines, including algebraic groups and Lie theory, automorphic forms, sheaf theory, finite groups, and homological algebra. It will interest mathematicians and graduate students in these and related subjects as an introduction to research in an area of increasing relevance and importance.
Book Synopsis Representations of Finite Dimensional Algebras and Related Topics in Lie Theory and Geometry by : Vlastimil Dlab
Download or read book Representations of Finite Dimensional Algebras and Related Topics in Lie Theory and Geometry written by Vlastimil Dlab and published by American Mathematical Soc.. This book was released on with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings are from the Tenth International Conference on Representations of Algebras and Related Topics (ICRA X) held at The Fields Institute. In addition to the traditional ''instructional'' workshop preceding the conference, there were also workshops on ''Commutative Algebra, Algebraic Geometry and Representation Theory'', ''Finite Dimensional Algebras, Algebraic Groups and Lie Theory'', and ''Quantum Groups and Hall Algebras''. These workshops reflect the latest developments and the increasing interest in areas that are closely related to the representation theory of finite dimensional associative algebras. Although these workshops were organized separately, their topics are strongly interrelated. The workshop on Commutative Algebra, Algebraic Geometry and Representation Theory surveyed various recently established connections, such as those pertaining to the classification of vector bundles or Cohen-Macaulay modules over Noetherian rings, coherent sheaves on curves, or ideals in Weyl algebras. In addition, methods from algebraic geometry or commutative algebra relating to quiver representations and varieties of modules were presented. The workshop on Finite Dimensional Algebras, Algebraic Groups and Lie Theory surveyed developments in finite dimensional algebras and infinite dimensional Lie theory, especially as the two areas interact and may have future interactions. The workshop on Quantum Groups and Hall Algebras dealt with the different approaches of using the representation theory of quivers (and species) in order to construct quantum groups, working either over finite fields or over the complex numbers. In particular, these proceedings contain a quite detailed outline of the use of perverse sheaves in order to obtain canonical bases. The book is recommended for graduate students and researchers in algebra and geometry.
Book Synopsis Multidimensional Analysis by : George W. Hart
Download or read book Multidimensional Analysis written by George W. Hart and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the mathematical properties of dimensioned quantities, such as length, mass, voltage, and viscosity. Beginning with a careful examination of how one expresses the numerical results of a measurement and uses these results in subsequent manipulations, the author rigorously constructs the notion of dimensioned numbers and discusses their algebraic structure. The result is a unification of linear algebra and traditional dimensional analysis that can be extended from the scalars to which the traditional analysis is perforce restricted to multidimensional vectors of the sort frequently encountered in engineering, systems theory, economics, and other applications.
Book Synopsis Classification and Identification of Lie Algebras by : Libor Šnob
Download or read book Classification and Identification of Lie Algebras written by Libor Šnob and published by American Mathematical Soc.. This book was released on 2017-04-05 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to serve as a tool for researchers and practitioners who apply Lie algebras and Lie groups to solve problems arising in science and engineering. The authors address the problem of expressing a Lie algebra obtained in some arbitrary basis in a more suitable basis in which all essential features of the Lie algebra are directly visible. This includes algorithms accomplishing decomposition into a direct sum, identification of the radical and the Levi decomposition, and the computation of the nilradical and of the Casimir invariants. Examples are given for each algorithm. For low-dimensional Lie algebras this makes it possible to identify the given Lie algebra completely. The authors provide a representative list of all Lie algebras of dimension less or equal to 6 together with their important properties, including their Casimir invariants. The list is ordered in a way to make identification easy, using only basis independent properties of the Lie algebras. They also describe certain classes of nilpotent and solvable Lie algebras of arbitrary finite dimensions for which complete or partial classification exists and discuss in detail their construction and properties. The book is based on material that was previously dispersed in journal articles, many of them written by one or both of the authors together with their collaborators. The reader of this book should be familiar with Lie algebra theory at an introductory level.
Book Synopsis Growth of Algebras and Gelfand-Kirillov Dimension by : G. R. Krause
Download or read book Growth of Algebras and Gelfand-Kirillov Dimension written by G. R. Krause and published by American Mathematical Soc.. This book was released on 2000 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the two decades that preceded the publication of the first edition of this book, the Gelfand-Kirillov dimension had emerged as a very useful and powerful tool for investigating non-commutative algebras. At that time, the basic ideas and results were scattered throughout various journal articles. The first edition of this book provided a much-needed reliable and coherent single source of information. Since that time, the book has become the standard reference source for researchers. For this edition, the authors incorporated the original text with only minor modifications. Errors have been corrected, items have been rephrased, and more mathematical expressions have been displayed for the purpose of clarity. The newly added Chapter 12 provides broad overviews of the new developments that have surfaced in the last few years, with references to the literature for details. The bibliography has been updated and accordingly, almost double the size of the original one. The faithful revision and contemporary design of this work offers time-honored expertise with modern functionality. A keenly appealing combination. So, whether for the classroom, the well-tended mathematical books collection, or the research desk, this book holds unprecedented relevance.
Book Synopsis Finite Dimensional Algebras by : Yurij A. Drozd
Download or read book Finite Dimensional Algebras written by Yurij A. Drozd and published by Berlin : Springer-Verlag. This book was released on 1994 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of finite dimensional algebras is one of the most fundamental domains of modern algebra, applied in several other parts of mathematics and in theoretical physics. The only prior knowledge assumed of the reader is linear algebra and, in places, a little group theory.
Book Synopsis Representations of Finite-Dimensional Algebras by : Peter Gabriel
Download or read book Representations of Finite-Dimensional Algebras written by Peter Gabriel and published by Springer Science & Business Media. This book was released on 1997-09-12 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "... [Gabriel and Roiter] are pioneers in this subject and they have included proofs for statements which in their opinions are elementary, those which will help further understanding and those which are scarcely available elsewhere. They attempt to take us up to the point where we can find our way in the original literature. ..." --The Mathematical Gazette
Book Synopsis Finite Dimensional Algebras and Quantum Groups by : Bangming Deng
Download or read book Finite Dimensional Algebras and Quantum Groups written by Bangming Deng and published by American Mathematical Soc.. This book was released on 2008 with total page 790 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The interplay between finite dimensional algebras and Lie theory dates back many years. In more recent times, these interrelations have become even more strikingly apparent. This text combines, for the first time in book form, the theories of finite dimensional algebras and quantum groups. More precisely, it investigates the Ringel-Hall algebra realization for the positive part of a quantum enveloping algebra associated with a symmetrizable Cartan matrix and it looks closely at the Beilinson-Lusztig-MacPherson realization for the entire quantum $\mathfrak{gl}_n$. The book begins with the two realizations of generalized Cartan matrices, namely, the graph realization and the root datum realization. From there, it develops the representation theory of quivers with automorphisms and the theory of quantum enveloping algebras associated with Kac-Moody Lie algebras. These two independent theories eventually meet in Part 4, under the umbrella of Ringel-Hall algebras. Cartan matrices can also be used to define an important class of groups--Coxeter groups--and their associated Hecke algebras. Hecke algebras associated with symmetric groups give rise to an interesting class of quasi-hereditary algebras, the quantum Schur algebras. The structure of these finite dimensional algebras is used in Part 5 to build the entire quantum $\mathfrak{gl}_n$ through a completion process of a limit algebra (the Beilinson-Lusztig-MacPherson algebra). The book is suitable for advanced graduate students. Each chapter concludes with a series of exercises, ranging from the routine to sketches of proofs of recent results from the current literature."--Publisher's website.
Book Synopsis Representations of Algebraic Groups, Quantum Groups, and Lie Algebras by : Georgia Benkart
Download or read book Representations of Algebraic Groups, Quantum Groups, and Lie Algebras written by Georgia Benkart and published by American Mathematical Soc.. This book was released on 2006 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers various aspects of the representation theory of Lie algebras, finite groups of Lie types, Hecke algebras, and Lie super algebras. This book outlines connections among irreducible representations of certain blocks of reduced enveloping algebras of semi-simple Lie algebras in positive characteristic.
Book Synopsis Numerical Calculations in Clifford Algebra by : Andrew Seagar
Download or read book Numerical Calculations in Clifford Algebra written by Andrew Seagar and published by John Wiley & Sons. This book was released on 2023-07-31 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: NUMERICAL CALCULATIONS IN CLIFFORD ALGEBRA An intuitive combination of the theory of Clifford algebra with numerous worked and computed examples and calculations Numerical Calculations in Clifford Algebra: A Practical Guide for Engineers and Scientists is an accessible and practical introduction to Clifford algebra, with comprehensive coverage of the theory and calculations. The book offers many worked and computed examples at a variety of levels of complexity and over a range of different applications making extensive use of diagrams to maintain clarity. The author introduces and documents the Clifford Numerical Suite, developed to overcome the limitations of existing computational packages and to enable the rapid creation and deployment of sophisticated and efficient code. Applications of the suite include Fourier transforms for arrays of any types of Clifford numbers and the solution of linear systems in which the coefficients are Clifford numbers of particular types, including scalars, bicomplex numbers, quaternions, Pauli matrices, and extended electromagnetic fields. Readers will find: A thorough introduction to Clifford algebra, with a combination of theory and practical implementation in a range of engineering problems Comprehensive explorations of a variety of worked and computed examples at various levels of complexity Practical discussions of the conceptual and computational tools for solving common engineering problems Detailed documentation on the deployment and application of the Clifford Numerical Suite Perfect for engineers, researchers, and academics with an interest in Clifford algebra, Numerical Calculations in Clifford Algebra: A Practical Guide for Engineers and Scientists will particularly benefit professionals in the areas of antenna design, digital image processing, theoretical physics, and geometry.
Book Synopsis Supersymmetries and Infinite-Dimensional Algebras by : N. H. March
Download or read book Supersymmetries and Infinite-Dimensional Algebras written by N. H. March and published by Academic Press. This book was released on 2013-10-22 with total page 651 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent devopments, particularly in high-energy physics, have projected group theory and symmetry consideration into a central position in theoretical physics. These developments have taken physicists increasingly deeper into the fascinating world of pure mathematics. This work presents important mathematical developments of the last fifteen years in a form that is easy to comprehend and appreciate.
Book Synopsis Infinite Dimensional Algebras and Quantum Integrable Systems by : Petr P. Kulish
Download or read book Infinite Dimensional Algebras and Quantum Integrable Systems written by Petr P. Kulish and published by Springer Science & Business Media. This book was released on 2006-01-17 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the invited lectures of the workshop "Infinite Dimensional Algebras and Quantum Integrable Systems" held in July 2003 at the University of Algarve, Faro, Portugal, as a satellite workshop of the XIV International Congress on Mathematical Physics. In it, recent developments in the theory of infinite dimensional algebras, and their applications to quantum integrable systems, are reviewed by leading experts in the field.
Book Synopsis Rings with Polynomial Identities and Finite Dimensional Representations of Algebras by : Eli Aljadeff
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.
Book Synopsis Finite-Dimensional Division Algebras over Fields by : Nathan Jacobson
Download or read book Finite-Dimensional Division Algebras over Fields written by Nathan Jacobson and published by Springer. This book was released on 2014-08-23 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here, the eminent algebraist, Nathan Jacobsen, concentrates on those algebras that have an involution. Although they appear in many contexts, these algebras first arose in the study of the so-called "multiplication algebras of Riemann matrices". Of particular interest are the Jordan algebras determined by such algebras, and thus their structure is discussed in detail. Two important concepts also dealt with are the universal enveloping algebras and the reduced norm. However, the largest part of the book is the fifth chapter, which focuses on involutorial simple algebras of finite dimension over a field.
Book Synopsis Elements of Algebra, Geometry and Mensuration, Reading Working Drawings, Measuring Instruments, Precision Measuring Instruments, General Appliances and Processes, Elementary Mechanics, Hydrostatics, Pneumatics, Geometry and Trigonometry, Natural Sines, Cosines, Tangents, and Cotangents, Table of Powers and Roots by :
Download or read book Elements of Algebra, Geometry and Mensuration, Reading Working Drawings, Measuring Instruments, Precision Measuring Instruments, General Appliances and Processes, Elementary Mechanics, Hydrostatics, Pneumatics, Geometry and Trigonometry, Natural Sines, Cosines, Tangents, and Cotangents, Table of Powers and Roots written by and published by . This book was released on 1922 with total page 808 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Book of Abstract Algebra by : Charles C Pinter
Download or read book A Book of Abstract Algebra written by Charles C Pinter and published by Courier Corporation. This book was released on 2010-01-14 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.
