LEADER 10137nam 2200541 450 001 996466544303316 005 20231110232308.0 010 $a3-030-63111-7 035 $a(CKB)4100000011807254 035 $a(MiAaPQ)EBC6524965 035 $a(Au-PeEL)EBL6524965 035 $a(OCoLC)1243263230 035 $a(PPN)254721567 035 $a(EXLCZ)994100000011807254 100 $a20211014d2021 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 00$aPolynomial identities in algebras /$fedited by Onofrio Mario Di Vincenzo and Antonio Giambruno 210 1$aCham, Switzerland :$cSpringer,$d[2021] 210 4$d©2021 215 $a1 online resource (424 pages) $cillustrations 225 1 $aSpringer INdAM ;$vv.44 311 $a3-030-63110-9 327 $aIntro -- 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 -- 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 Poincare? 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. 327 $a5.2 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 n?4 -- 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 -- 5 Commuting Inner b-Generalized Skew Derivations -- 6 Commuting b-Generalized Derivations on Multilinear Polynomials -- 7 The Main Result -- 7.1 Let d and ? be C-Linearly Independent Modulo SDint -- 7.2 Let d and ? be C-Linearly Dependent Modulo SDint -- 8 Some Open Problems -- References -- Relatively Free Algebras of Finite Rank -- 1 Introduction -- 2 Models for Relatively Free Algebras -- 3 General Remarks -- 4 Polynomial Identities for UT2(G(k)) -- 4.1 The Case UT2(G(2m)), for 1?m?2 -- 5 Polynomial Identities for Fk(UT2(G)) -- 6 Conclusion -- References -- Graded Algebras, Algebraic Functions, Planar Trees, and Elliptic Integrals -- 1 Introduction -- 2 Growth of Algebras and Hilbert Series -- 3 Algebras with Prescribed Hilbert Series -- 4 PI-Algebras -- 5 Algebraic and Transcendental Power Series. 327 $a6 Planar Rooted Trees and Algebraic Series -- 7 Noncommutative Invariant Theory -- References -- Central Polynomials of Algebras and Their Growth -- 1 Introduction -- 2 A General Setting -- 3 Examples of Central Polynomials -- 4 Algebras Without Proper Central Polynomials -- 5 The Proper Central Exponent -- 6 The Central Exponent -- 7 Non Associative Algebras -- References -- Trace Identities on Diagonal Matrix Algebras -- 1 Introduction -- 2 Preliminaries -- 3 Matrix Algebras with Trace -- 4 Some Results on Dn -- 5 Trace Identities on D2 -- 6 Trace Identities on D3 -- References -- Codimension Growth for Weak Polynomial Identities, and Non-integrality of the PI Exponent -- 1 Introduction -- 2 Preliminaries -- 2.1 Generalities -- 2.2 Polynomial Identities -- 2.3 Multilinear Polynomials. Modules over the Symmetric Group -- 2.4 The Exponent -- 2.5 The Action of the General Linear Group -- 2.6 Special Pairs and Pairs of Associative Type -- 3 Polynomial Growth of the Codimensions -- 3.1 Slow Growth of the Codimensions -- 3.2 Characterizing Varieties of Pairs of Polynomial Growth -- 3.3 Almost Polynomial Growth -- 3.3.1 The Pair (UT2,UT2(-)) -- 3.3.2 The Pair (E,E(-)) -- 3.3.3 The Pair (M2,sl2) -- 3.3.4 More Examples -- 4 Graded Pairs and Amitsur's Conjecture -- 4.1 Weak Graded Polynomial Identities -- 4.2 Finitely Generated Superpairs -- 4.3 Non-integral Exponent: An Example -- References -- On Codimensions of Algebras with Involution -- 1 Introduction -- 2 *-Codimensions and *-Fundamental Algebras -- 3 Low Exponential Growth -- References -- Context-Free Languages and Associative Algebras with Algebraic Hilbert Series -- 1 Introduction -- 2 Preliminaries -- 2.1 Associative Algebras and Their Hilbert Series -- 2.2 The Homology and Hilbert Series of Monomial Algebras -- 2.3 Automaton Algebras and Homologically Unambiguous Algebras. 327 $a3 Finitely Presented Algebras Associated to Context-Free Languages -- 3.1 The General Construction -- 3.2 Graded Algebras Examples -- References -- On Almost Nilpotent Varieties of Linear Algebras -- 1 Introduction -- 2 Almost Nilpotent Varieties Generated by One or Two Dimensional Algebra -- 3 Almost Nilpotent Varieties and Skew Symmetric Polynomials -- 4 A Commutative Metabelian Algebra with Skew Symmetric Polynomials (a Jordan Algebra) -- 5 Anti-Commutative Metabelian Algebra with Skew Symmetric Polynomials -- 6 A Characterization of Almost Nilpotent Varieties in Different Classes of Algebras -- 7 An Infinite Series of Almost Nilpotent Metabelian Varieties with Polynomial Growth -- 8 Almost Nilpotent Varieties with Exponentional Growth -- References -- (?,)-Differential Identities of UTm(F) -- 1 Introduction -- 2 The Problem -- 3 The Coupled Actions of ? and on UTm(F) -- 4 The Separate Actions of ? and on UTm(F) -- 5 Behind the Scenes -- References -- Identities in Group Rings, Enveloping Algebras and Poisson Algebras -- 1 Introduction -- 2 Identical Relations of Group Rings -- 3 Identical Relations of Enveloping Algebras -- 4 Poisson Algebras and Their Identities -- 4.1 Poisson Algebras -- 4.2 Examples of Poisson Algebras -- 4.3 Poisson Identities -- 5 Multilinear Identities of Symmetric Poisson Algebras -- 6 Lie Identities of Symmetric Poisson Algebras -- 6.1 Lie Nilpotence of Truncated Symmetric Algebras s(L) -- 6.2 Solvability of Truncated Symmetric Algebras s(L) -- 6.3 Nilpotency and Solvability of Symmetric Algebras S(L) -- 6.4 Delta-Sets and Multilinear Poisson Identical Relations -- 6.5 Products of Commutators in Poisson Algebras -- 6.6 Solvability of Symmetric Algebras s(L) and S(L) in Case Char K = 2 -- References -- Notes on the History of Identities on Group (and Loop) Algebras -- 1 Introduction. 327 $a2 Existence of Polynomial Identities -- 3 Group Theoretical Properties of Unit Groups -- 4 Group Indentities -- 5 Loop Algebras -- References -- Cayley Hamilton Algebras -- 1 Introduction -- 2 The Cayley-Hamilton Identity -- 3 The First and Second Fundamental Theorem -- 3.1 The Free Trace Algebra -- 3.3 A Characteristic Free Approach -- 3.12 Symbolic Approach -- 3.12.1 The Approach of Zieplies and Vaccarino -- References -- Growth of Differential Identities -- 1 Introduction -- 2 L-Algebras and Differential Identities -- 3 On Algebras with Derivations of Polynomial Growth -- 4 The Algebra of 2 x 2 Upper Triangular Matrices and Its Differential Identities -- 5 On Differential Identities of the Grassmann Algebra -- References -- Derived Lengths of Symmetric Poisson Algebras -- 1 Introduction -- 2 Definitions and Notation -- 3 The Lie Structure of Enveloping Algebras -- 4 Symmetric Poisson Algebras Satisfying a Poisson Identity -- 5 Lie Nilpotence and Solvability of S(L) and s(L) -- 6 Derived Lengths of s(L) -- References -- Group and Polynomial Identities in Group Rings -- 1 Introduction -- 2 -Group Identities for U(FG) -- 3 Group Identities for Unitary Units of FG -- References. 410 0$aSpringer INdAM 606 $aPI-algebras$vCongresses 606 $aAnells associatius$2thub 608 $aCongressos$2thub 608 $aLlibres electrònics$2thub 615 0$aPI-algebras 615 7$aAnells associatius 676 $a512.4 702 $aDi Vincenzo$b Onofrio Mario 702 $aGiambruno$b A. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466544303316 996 $aPolynomial identities in algebras$91897489 997 $aUNISA LEADER 04472nam 22006614a 450 001 9910971850403321 005 20251116160644.0 010 $a9780309173537 010 $a0309173531 010 $a9780309525190 010 $a0309525195 035 $a(CKB)111069351117046 035 $a(SSID)ssj0000280775 035 $a(PQKBManifestationID)11240794 035 $a(PQKBTitleCode)TC0000280775 035 $a(PQKBWorkID)10300167 035 $a(PQKB)11656686 035 $a(MiAaPQ)EBC3375689 035 $a(Au-PeEL)EBL3375689 035 $a(CaPaEBR)ebr10041109 035 $a(OCoLC)923258136 035 $a(Perlego)4734970 035 $a(BIP)53859985 035 $a(BIP)7361249 035 $a(EXLCZ)99111069351117046 100 $a20010710d2001 uy 0 101 0 $aeng 135 $aurcn||||||||| 181 $ctxt 182 $cc 183 $acr 200 00$aInformation systems and the environment /$fedited by Deanna J. Richards, Braden R. Allenby, and W. Dale Compton 205 $a1st ed. 210 $aWashington, D.C. $cNational Academy Press$dc2001 215 $aviii, 228 p. $cill 300 $a"National Academy of Engineering." 300 $aBased on July 1997 workshop. 311 08$a9780309062435 311 08$a0309062438 320 $aIncludes bibliographical references and index. 327 $aFront Matter -- Preface -- Contents -- Information Systems and the Environment Overview and Perspectives -- The Information Technology Revolution and Industrial Ecology -- The Information Revolution and Sustainability Mutually Reinforcing Dimensions of the Human Future -- Intellectual Property Rights in Data -- Information Systems within the Firm -- Improving Environmental Knowledge Sharing -- Using Environmental Knowledge Systems at DuPont -- Environmental Information Management Systems at Rhône-Poulenc -- Environmental Knowledge-Sharing in Manufacturing -- Modular Design for Recyclability Implementation and Knowledge Dissemination -- Environmental Information in Supply-Chain Design and Coordination -- Simulation Models for Information Sharing and Collaboration -- Opportunities for Collaboration and New Technologies -- Industrial Research and Development Collaborations Increasing Environmental Knowledge for Competitive Advantage -- InfoSleuth An Emerging Technology for Sharing Distributed Environmental Information -- Public Access to Environmental Information -- Internet Global Environmental Information Sharing -- Knowledge Networking for Global Sustainability -- Biographical Data -- Index. 330 $aInformation technology is a powerful tool for meeting environmental objectives and promoting sustainable development. This collection of papers by leaders in industry, government, and academia explores how information technology can improve environmental performance by individual firms, collaborations among firms, and collaborations among firms, government agencies, and academia. Information systems can also be used by nonprofit organizations and the government to inform the public about broad environmental issues and environmental conditions in their neighborhoods. Several papers address the challenges to information management posed by the explosive increase in information and knowledge about environmental issues and potential solutions, including determining what information is environmentally relevant and how it can be used in decision making. In addition, case studies are described and show how industry is using information systems to ensure sustainable development and meet environmental standards. The book also includes examples from the public sector showing how governments use information knowledge systems to disseminate "best practices" beyond big firms to small businesses, and from the world of the Internet showing how knowledge is shared among environmental advocates and the general public. 606 $aEnvironmental protection 606 $aEnvironmental education 615 0$aEnvironmental protection. 615 0$aEnvironmental education. 676 $a363.7/05 701 $aRichards$b Deanna J$01808304 701 $aAllenby$b Braden R$0872201 701 $aCompton$b W. Dale$050453 712 02$aNational Academy of Engineering. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910971850403321 996 $aInformation systems and the environment$94365316 997 $aUNINA