Algebraic Quotients Torus Actions And Cohomology The Adjoint Representation And The Adjoint Action

Author: A. Bialynicki-Birula
Publisher: Springer Science & Business Media
ISBN: 9783540432111
Size: 35.72 MB
Format: PDF, ePub, Docs
View: 2953
Download
This is the second volume of the new subseries "Invariant Theory and Algebraic Transformation Groups". The aim of the survey by A. Bialynicki-Birula is to present the main trends and achievements of research in the theory of quotients by actions of algebraic groups. This theory contains geometric invariant theory with various applications to problems of moduli theory. The contribution by J. Carrell treats the subject of torus actions on algebraic varieties, giving a detailed exposition of many of the cohomological results one obtains from having a torus action with fixed points. Many examples, such as toric varieties and flag varieties, are discussed in detail. W.M. McGovern studies the actions of a semisimple Lie or algebraic group on its Lie algebra via the adjoint action and on itself via conjugation. His contribution focuses primarily on nilpotent orbits that have found the widest application to representation theory in the last thirty-five years.

Actions And Invariants Of Algebraic Groups Second Edition

Author: Walter Ricardo Ferrer Santos
Publisher: CRC Press
ISBN: 1351644777
Size: 40.93 MB
Format: PDF, Docs
View: 285
Download
Actions and Invariants of Algebraic Groups, Second Edition presents a self-contained introduction to geometric invariant theory starting from the basic theory of affine algebraic groups and proceeding towards more sophisticated dimensions." Building on the first edition, this book provides an introduction to the theory by equipping the reader with the tools needed to read advanced research in the field. Beginning with commutative algebra, algebraic geometry and the theory of Lie algebras, the book develops the necessary background of affine algebraic groups over an algebraically closed field, and then moves toward the algebraic and geometric aspects of modern invariant theory and quotients.

Newsletter

Author: New Zealand Mathematical Society
Publisher:
ISBN:
Size: 69.81 MB
Format: PDF
View: 858
Download

Algebraic Quotients Torus Actions And Cohomology The Adjoint Representation And The Adjoint Action

Author: A. Bialynicki-Birula
Publisher: Springer Science & Business Media
ISBN: 3662050714
Size: 17.81 MB
Format: PDF, ePub, Docs
View: 144
Download
This is the second volume of the new subseries "Invariant Theory and Algebraic Transformation Groups". The aim of the survey by A. Bialynicki-Birula is to present the main trends and achievements of research in the theory of quotients by actions of algebraic groups. This theory contains geometric invariant theory with various applications to problems of moduli theory. The contribution by J. Carrell treats the subject of torus actions on algebraic varieties, giving a detailed exposition of many of the cohomological results one obtains from having a torus action with fixed points. Many examples, such as toric varieties and flag varieties, are discussed in detail. W.M. McGovern studies the actions of a semisimple Lie or algebraic group on its Lie algebra via the adjoint action and on itself via conjugation. His contribution focuses primarily on nilpotent orbits that have found the widest application to representation theory in the last thirty-five years.

Computational Commutative Algebra 1

Author: Martin Kreuzer
Publisher: Springer Science & Business Media
ISBN: 354067733X
Size: 68.94 MB
Format: PDF, Kindle
View: 3662
Download
This accessible introduction to Grobner bases and their applications helps bridge the gap between theoretical computer algebra and actual computation. It includes 44 tutorials and 165 exercises as well as other numerous amusements.

Finite Dimensional Algebras And Quantum Groups

Author: Bangming Deng
Publisher: American Mathematical Soc.
ISBN: 0821841866
Size: 56.63 MB
Format: PDF, ePub, Docs
View: 4742
Download
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.

Basic Noncommutative Geometry

Author: Masoud Khalkhali
Publisher: European Mathematical Society
ISBN: 9783037190616
Size: 18.20 MB
Format: PDF, ePub, Docs
View: 7410
Download
"Basic Noncommutative Geometry provides an introduction to noncommutative geometry and some of its applications. The book can be used either as a textbook for a graduate course on the subject or for self-study. It will be useful for graduate students and researchers in mathematics and theoretical physics and all those who are interested in gaining an understanding of the subject. One feature of this book is the wealth of examples and exercises that help the reader to navigate through the subject. While background material is provided in the text and in several appendices, some familiarity with basic notions of functional analysis, algebraic topology, differential geometry and homological algebra at a first year graduate level is helpful. Developed by Alain Connes since the late 1970s, noncommutative geometry has found many applications to long-standing conjectures in topology and geometry and has recently made headways in theoretical physics and number theory. The book starts with a detailed description of some of the most pertinent algebra-geometry correspondences by casting geometric notions in algebraic terms, then proceeds in the second chapter to the idea of a noncommutative space and how it is constructed. The last two chapters deal with homological tools: cyclic cohomology and Connes-Chern characters in K-theory and K-homology, culminating in one commutative diagram expressing the equality of topological and analytic index in a noncommutative setting. Applications to integrality of noncommutative topological invariants are given as well."--Publisher's description.

Cox Rings

Author: Ivan Arzhantsev
Publisher: Cambridge University Press
ISBN: 1316147959
Size: 54.90 MB
Format: PDF, ePub, Mobi
View: 4810
Download
Cox rings are significant global invariants of algebraic varieties, naturally generalizing homogeneous coordinate rings of projective spaces. This book provides a largely self-contained introduction to Cox rings, with a particular focus on concrete aspects of the theory. Besides the rigorous presentation of the basic concepts, other central topics include the case of finitely generated Cox rings and its relation to toric geometry; various classes of varieties with group actions; the surface case; and applications in arithmetic problems, in particular Manin's conjecture. The introductory chapters require only basic knowledge in algebraic geometry. The more advanced chapters also touch on algebraic groups, surface theory, and arithmetic geometry. Each chapter ends with exercises and problems. These comprise mini-tutorials and examples complementing the text, guided exercises for topics not discussed in the text, and, finally, several open problems of varying difficulty.

Differential Geometrical Theory Of Statistics

Author: Frédéric Barbaresco
Publisher: MDPI
ISBN: 3038424242
Size: 69.68 MB
Format: PDF, Docs
View: 2220
Download
This book is a printed edition of the Special Issue "Differential Geometrical Theory of Statistics" that was published in Entropy