Title Polynomial identities in algebras / Onofrio Mario Di Vincenzo, Antonio Giambruno, editors

Published Cham, Switzerland : Springer, [2021]

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Description 1 online resource (ix, 421 pages) : illustrations Series Springer INdAM series, 2281-518X ; volume 44 Springer INdAM series ; v. 44. 2281-518X Contents 880-01 Intro -- Preface -- Contents -- About the Editors -- Some Thoughts on the Current State of the Theory of Identical Relations in Lie Algebras -- 1 Introduction -- 2 Finite Basis Problem -- 3 Engel Lie Algebras -- 3.1 Global Nilpotence -- 3.2 Restricted Burnside Problem: Local Nilpotence of Engel Lie algebras -- 4 Identities of Simple Lie Algebras -- 4.1 The Isomorphism Problem -- 4.2 Identities of Cartan Type Lie Algebras -- 4.3 Capelli Identities -- 5 Codimension Growth -- 5.1 Exponential Growth -- 5.2 Overexponential Growth -- 5.3 Colength -- 6 Graded Lie Algebras and Identities 880-01/(S Some thoughts on the current state on the theory of identical relations in Lie algebras -- Minimal degree of identities of matrix algebras with additional structures -- On the asymptotics of Capelli polynomials -- Regev's conjecture for algebras with Hopf actions -- l-Weak identities and central polynomials for matrices -- Computing multiplicities in the sign trace cocharacters of M12 (F) -- b-Generalized skew derivations on multilinear polynomials in prime rings -- Relatively free algebras of finite rank -- Graded algebras, algebraic functions, planar trees and elliptic integrals -- Central polynomials of algebras and their growth -- Trace identities on diagonal matrix algebras -- Codimension growth for weak polynomial identities, and non-integrality of the PI exponent -- On codimensions of algebras with involution -- Context-free languages and associative algebras with algebraic Hilbert series -- On almost nilpotent varieties of linear algebras -- (δ, ε)-Differential identities of UTm(F) -- Identities in group rings, enveloping algebras and Poisson algebras -- Notes on the history of identities on group (and loop) algebras -- Cayley Hamilton algebras -- Growth of differential identities -- Derived lengths of symmetric Poisson algebras -- Group and polynomial identities in group rings 7 Graded Identities of Lie Algebras and Generalizations -- 7.1 Codimension Growth -- 7.2 Isomorphism of H-Algebras -- 8 Special Lie Algebras -- References -- Minimal Degree of Identities of Matrix Algebras with Additional Structures -- 1 Introduction -- 2 Involution Case -- 3 Graded Case -- 4 Graded Involution Case -- References -- On the Asymptotics of Capelli Polynomials -- 1 Introduction -- 2 Ordinary Case -- 3 Z2-Graded Case -- 4 Involution Case -- 4.1 -Capelli Polynomials and the -Algebra UT(A1 ..., An) -- 4.2 Asymptotics for -Capelli Polynomials -- References Regev's Conjecture for Algebras with Hopf Actions -- 1 Introduction -- 2 Regev's Conjectures for Algebras Without Actions -- 2.1 Background on Magnums -- 2.2 Codimension Sequences -- 3 H-Cocharacters -- 4 Rationality of Poincaré Series -- 5 Young Derived Sequences -- References -- Weak Identities and Central Polynomials for Matrices -- 1 Introduction -- 2 Preliminaries -- 2.1 Identities, Central Polynomials and Examples -- 2.2 Spechtian Polynomials -- 3 Weak Identities -- 3.1 Weak and Strong Variables -- 3.2 Modules of Weak Identities -- 4 Central Polynomials for Matrices 4.1 -Weak Central Polynomials -- 5 The Connection to the Representation Theory -- 5.1 Identities and the Group Algebra -- 5.2 Identities and Representations -- 6 Weak Identities and the Case n = 2 -- 6.1 Polynomials of Degree m = 2 -- 6.2 Weak Identities of Degree m = 3 -- 6.3 Weak Identities of Degree m = 4 -- 7 The Weak PI-Degree of M3(F) -- 7.1 Fields of Characteristic Not 3 -- 7.2 The Case char F=3 -- 8 Weak Identities for M3(F) in Degree 6 -- 8.1 Weak Identities of M3(F) -- 8.2 Halpin's Identity and Its Projections -- 8.3 Identities from the Okubo Algebra -- 9 Matrices of Size ne." 9.1 Shadows of Identities -- 9.2 Weak Identities Degree 2n -- References -- Computing Multiplicities in the Sign Trace Cocharacters of M2,1(F) -- 1 Introduction -- 2 Reduced Notation -- 3 The Sign Trace Cocharacter of M2,1(F) -- 3.1 Computation of the Coefficient for {n-2,2} -- 4 The Final Result -- References -- b-Generalized Skew Derivations on Multilinear Polynomials in Prime Rings -- 1 Introduction -- 2 Some Results on Differential Identities with Automorphisms -- 3 Commuting Generalized Derivations and Commuting Generalized Skew Derivations -- 4 Some Remarks on Matrix Algebras Summary This volume contains the talks given at the INDAM workshop entitled "Polynomial identites in algebras", held in Rome in September 2019. The purpose of the book is to present the current state of the art in the theory of PI-algebras. The review of the classical results in the last few years has pointed out new perspectives for the development of the theory. In particular, the contributions emphasize on the computational and combinatorial aspects of the theory, its connection with invariant theory, representation theory, growth problems. It is addressed to researchers in the field Subject PI-algebras -- Congresses Álgebra PI-algebras Anells associatius. Genre/Form proceedings (reports) Conference papers and proceedings Conference papers and proceedings. Actes de congrès. Congressos. Llibres electrònics. Form Electronic book Author Di Vincenzo, Onofrio Mario, editor Giambruno, A., editor. Istituto nazionale di alta matematica Francesco Severi, sponsoring body. ISBN 9783030631116 3030631117

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