گروه‌ها، جبرها و کاربردها: هجدهمین کنگره جبر آمریکای لاتین، 3-8 اوت 2009، سائو پدرو، اسپ، برزیل (ریاضیات معاصر)

This book contains the proceedings of the XVIII Latin American Algebra Colloquium, held from August 3-8, 2009, in Sao Paulo, Brazil. It includes research articles as well as up-to-date surveys covering several directions of current research in algebra, such as Asymptotic Codimension Growth, Hopf Algebras, Structure Theory of both Associative and Non-Associative Algebras, Partial Actions of Groups on Rings, and contributions to Coding Theory Contents 6 Preface 8 Linear codes over Fq[u]/(ut) 10 Globalization theorems for partial Hopf (co)actions, and some of their applications 22 On Nichols algebras associated to simple racks 40 Pointed Hopf algebras with standard braiding are generated in degree one 66 Asymptotics of Young tableaux in the (k,l) hook 80 Classification of irreducible representations over finite simple Lie conformal superalgebras 94 1. Introduction 94 2. Formal distributions, Lie conformal superalgebras and their modules 96 3. Lie conformal superalgebra K0, K1 and Cur g and its finite irreducible representations. 102 4. Lie conformal superalgebra Wn and finite irreducible representations. 106 5. Lie conformal superalgebra Sn and its finite irreducible modules 116 6. Lie conformal superalgebras Sn,b and Sn, and their finite irreducible modules 119 7. Lie conformal superalgebra Kn and its finite irreducible modules 120 8. Work in progress 129 References 129 Pure gaps and bounds for the generalized Hamming weights of Goppa codes 132 Exact divisibility of exponential sums over the binary field via the covering method 138 All hereditary torsion theories are higher differential 146 A categorical approach to classical and quantum Schur–Weyl duality 152 1. Introduction 153 2. Sequences of algebras and monoidal categories 155 3. Symmetric groups and general linear Lie algebras 160 4. Hecke algebras and quantized enveloping algebras 161 5. Affine symmetric groups and loop algebras 163 6. Yangians and degenerate affine Hecke algebras 166 7. Quantum affine algebras and affine Hecke algebras 171 8. Localizations and categorical actions 174 References 179 Partial actions: a survey 182 On free associative algebras linearly graded by finite groups 194 Gelfand-Tsetlin categories 202 On growth of codimensions of Jordan algebras 214 Geometric Weil representations for star-analogues of SL(2, k) 220 Exceptional sequences, braid groups and clusters 236 Introduction 236 1. Topological AR-quivers 237 2. Theorem of Brady-Watt and Bessis 238 3. Exceptional sequences 239 4. Theorems about exceptional sequences 242 5. Appendix 244 References 249 Spherical distributions of some generalized Gelfand pairs attached to the Heisenberg group 250 On the linearity and quasi-cyclicity of the Gray image of codes over a Galois ring 264 Some applications of Frobenius algebras to Hopf algebras 278 The algebra of differential operators associated to a weight matrix: A first example 300 Machine Generated Contents Note: Linear Codes Over Fq[u]/(ut) / R. Alfaro -- Globalization Theorems For Partial Hopf (co)actions, And Some Of Their Applications / E. Batista -- On Nichols Algebras Associated To Simple Racks / L. Vendramin -- Pointed Hopf Algebras With Standard Braiding Are Generated In Degree One / A. Garcia Iglesias -- Asymptotics Of Young Tableaux In The (k, L) Hook / A. Regev -- Classification Of Irreducible Representations Over Finite Simple Lie Conformal Superalgebras / J.i. Liberati -- Pure Gaps And Bounds For The Generalized Hamming Weights Of Goppa Codes / C. Carvalho -- Exact Divisibility Of Exponential Sums Over The Binary Field Via The Covering Method / I.m. Rubio -- All Hereditary Torsion Theories Are Higher Differential / A. Sant'ana. A Categorical Approach To Classical And Quantum Schur-weyl Duality / A. Molev -- Partial Actions: A Survey / M. Dokuchaev -- On Free Associative Algebras Linearly Graded By Finite Groups / L.s.i. Murakami -- Gelfand-tsetlin Categories / M. Saorin -- On Growth Of Codimensions Of Jordan Algebras / E. Zelmanov -- Geometric Weil Representations For Star-analogues Of Sl(2, & Kappa;) / J. Soto-andrade -- Exceptional Sequences, Braid Groups And Clusters / K. Igusa -- Spherical Distributions Of Some Generalized Gelfand Pairs Attached To The Heisenberg Group / L. Saal -- On The Linearity And Quasi-cyclicity Of The Gray Image Of Codes Over A Galois Ring / H. Tapia-recillas -- Some Applications Of Frobenius Algebras To Hopf Algebras / M. Lorenz. César Polcino Milies, Editor. Includes Bibliographical References. Machine generated contents note: Linear codes over Fq[u]/(ut) -- R. Alfaro Globalization theorems for partial Hopf (co)actions, and some of their applications -- E. Batista On Nichols algebras associated to simple racks -- L. Vendramin Pointed Hopf algebras with standard braiding are generated in degree one -- A. Garcia Iglesias Asymptotics of Young tableaux in the (k,l) hook -- A. Regev Classification of irreducible representations over finite simple Lie conformal superalgebras -- J.I. Liberati Pure gaps and bounds for the generalized Hamming weights of Goppa codes -- C. Carvalho Exact divisibility of exponential sums over the binary field via the covering method -- I. M. Rubio All hereditary torsion theories are higher differential -- A. Sant'Ana A categorical approach to classical and quantum Schur-Weyl duality -- A. Molev Partial actions: a survey -- M. Dokuchaev On free associative algebras linearly graded by finite groups -- L. S. I. Murakami Gelfand-Tsetlin categories -- M. Saorin On growth of codimensions of Jordan algebras -- E. Zelmanov Geometric Weil representations for star-analogues of SL(2, κ) -- J. Soto-Andrade Exceptional sequences, braid groups and clusters -- K. Igusa Spherical distributions of some generalized Gelfand pairs attached to the Heisenberg group -- L. Saal On the linearity and quasi-cyclicity of the Gray image of codes over a Galois ring -- H. Tapia-Recillas Some applications of Frobenius algebras to Hopf algebras -- M. Lorenz. This book contains the proceedings of the XVIII Latin American Algebra Colloquium, held from August 3–8, 2009, in São Paulo, Brazil. It includes research articles as well as up-to-date surveys covering several directions of current research in algebra, such as Asymptotic Codimension Growth, Hopf Algebras, Structure Theory of both Associative and Non-Associative Algebras, Partial Actions of Groups on Rings, and contributions to Coding Theory.