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010   $a3-662-55350-3
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100   $a20170909d2017      u|         0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aAlgebraic Theory of Locally Nilpotent Derivations /$fby Gene Freudenburg
205   $a2nd ed. 2017.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2017.
215   $a1 online resource (XXII, 319 p.) 
225 1 $aEncyclopaedia of Mathematical Sciences ;$v136
311 08$a3-662-55348-1 
320   $aIncludes bibliographical references and index.
327   $aIntroduction -- 1 First Principles -- 2 Further Properties of LNDs -- 3 Polynomial Rings -- 4 Dimension Two -- 5 Dimension Three -- 6 Linear Actions of Unipotent Groups -- 7 Non-Finitely Generated Kernels -- 8 Algorithms -- 9 Makar-Limanov and Derksen Invariants -- 10 Slices, Embeddings and Cancellation -- 11 Epilogue -- References -- Index.
330   $aThis book explores the theory and application of locally nilpotent derivations, a subject motivated by questions in affine algebraic geometry and having fundamental connections to areas such as commutative algebra, representation theory, Lie algebras and differential equations. The author provides a unified treatment of the subject, beginning with 16 First Principles on which the theory is based. These are used to establish classical results, such as Rentschler's Theorem for the plane and the Cancellation Theorem for Curves. More recent results, such as Makar-Limanov's theorem for locally nilpotent derivations of polynomial rings, are also discussed. Topics of special interest include progress in classifying additive actions on three-dimensional affine space, finiteness questions (Hilbert's 14th Problem), algorithms, the Makar-Limanov invariant, and connections to the Cancellation Problem and the Embedding Problem. A lot of new material is includedin this expanded second edition, such as canonical factorization of quotient morphisms, and a more extended treatment of linear actions. The reader will also find a wealth of examples and open problems and an updated resource for future investigations.
410  0$aEncyclopaedia of Mathematical Sciences ;$v136
606   $aCommutative algebra
606   $aCommutative rings
606   $aAlgebraic geometry
606   $aTopological groups
606   $aLie groups
606   $aCommutative Rings and Algebras
606   $aAlgebraic Geometry
606   $aTopological Groups and Lie Groups
615  0$aCommutative algebra.
615  0$aCommutative rings.
615  0$aAlgebraic geometry.
615  0$aTopological groups.
615  0$aLie groups.
615 14$aCommutative Rings and Algebras.
615 24$aAlgebraic Geometry.
615 24$aTopological Groups and Lie Groups.
676   $a512.44
700   $aFreudenburg$b Gene$4aut$4http://id.loc.gov/vocabulary/relators/aut$0624596
906   $aBOOK
912   $a9910768450203321
996   $aAlgebraic theory of locally nilpotent derivations$91098820
997   $aUNINA