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1. Computational invariant theory [2002]
 Derksen, Harm, 1970
 Berlin ; New York : Springer, c2002.
 Description
 Book — x, 268 p. : ill. ; 25 cm.
 Summary

 Preface.
 1. Constructive Ideal Theory.
 2. Invariant Theory.
 3. Invariant Theory of Finite Groups.
 4. Invariant Theory of Reductive Groups.
 5. Applications of Invariant Theory. Bibliography. Index.
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QA201 .D47 2002  Available 
 Freudenburg, Gene, author.
 Second edition.  Berlin, Germany : Springer, [2017]
 Description
 Book — xxii, 319 pages : illustrations ; 25 cm.
 Summary

 Introduction.
 1 First Principles.
 2 Further Properties of LNDs.
 3 Polynomial Rings.
 4 Dimension Two.
 5 Dimension Three.
 6 Linear Actions of Unipotent Groups.
 7 NonFinitely Generated Kernels.
 8 Algorithms.
 9 MakarLimanov and Derksen Invariants.
 10 Slices, Embeddings and Cancellation.
 11 Epilogue. References. Index.
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QA564 .F75 2017  Unknown 
 Freudenburg, Gene, author.
 Cham : Springer, [2017]
 Description
 Book — 1 online resource.
 Summary

 Introduction.
 1 First Principles.
 2 Further Properties of LNDs.
 3 Polynomial Rings.
 4 Dimension Two.
 5 Dimension Three.
 6 Linear Actions of Unipotent Groups.
 7 NonFinitely Generated Kernels.
 8 Algorithms.
 9 MakarLimanov and Derksen Invariants.
 10 Slices, Embeddings and Cancellation.
 11 Epilogue. References. Index.
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 Timashev, Dmitry A.
 Berlin ; New York : Springer, c2011.
 Description
 Book — xxi, 253 p. : ill. ; 24 cm.
 Summary

 Introduction.
 1 Algebraic Homogeneous Spaces.
 2 Complexity and Rank.
 3 General Theory of Embeddings.
 4 Invariant Valuations.
 5 Spherical Varieties. Appendices. Bibliography. Indices.
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QA387 .T56 2011  Unknown 
5. Computational invariant theory [2015]
 Derksen, Harm, 1970
 Second enlarged edition / with two appendices by Vladimir L. Popov, and an addendum by Norbert A. Campo and Vladimir L. Popov.  Heidelberg ; New York : Springer Verlag, c2015.
 Description
 Book — xxii, 366 p. : ill. ; 25 cm.
 Summary

This book is about the computational aspects of invariant theory. Of central interest is the question how the invariant ring of a given group action can be calculated. Algorithms for this purpose form the main pillars around which the book is built. There are two introductory chapters, one on Grobner basis methods and one on the basic concepts of invariant theory, which prepare the ground for the algorithms. Then algorithms for computing invariants of finite and reductive groups are discussed. Particular emphasis lies on interrelations between structural properties of invariant rings and computational methods. Finally, the book contains a chapter on applications of invariant theory, covering fields as disparate as graph theory, coding theory, dynamical systems, and computer vision. The book is intended for postgraduate students as well as researchers in geometry, computer algebra, and, of course, invariant theory. The text is enriched with numerous explicit examples which illustrate the theory and should be of more than passing interest. More than ten years after the first publication of the book, the second edition now provides a major update and covers many recent developments in the field. Among the roughly 100 added pages there are two appendices, authored by Vladimi r Popov, and an addendum by Norbert A'Campo and Vladimir Popov.
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QA201 .D47 2015  Unknown 
 Lakshmibai, V. (Venkatramani)
 Berlin : Springer, c2008.
 Description
 Book — xiv, 265 p.
7. Modular invariant theory [2011]
 Campbell, H. E. A. Eddy (Harold Edward Alexander Eddy), 1954
 Heidelberg ; New York : Springer, c2011.
 Description
 Book — xiii, 233 p. ; 24 cm.
 Summary

 1 First Steps.
 2 Elements of Algebraic Geometry and Commutative Algebra.
 3 Applications of Commutative Algebra to Invariant Theory.
 4 Examples.
 5 Monomial Orderings and SAGBI Bases.
 6 Block Bases.
 7 The Cyclic Group Cp.
 8 Polynomial Invariant Rings.
 9 The Transfer.
 10 Invariant Rings via Localization.
 11 Rings of Invariants which are Hypersurfaces.
 12 Separating Invariants.
 13 Using SAGBI Bases to Compute Rings of Invariants.
 14 Ladders. References. Index.
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QA177 .C36 2011  Unknown 
 Lakshmibai, V. (Venkatramani)
 Berlin : Springer, c2008.
 Description
 Book — xiv, 265 p. : ill. ; 25 cm.
 Online

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QA564 .K35 2008  Available 
 Freudenburg, Gene.
 Berlin ; New York : SpringerVerlag, c2006.
 Description
 Book — xi, 261 p. : ill. ; 24 cm.
 Summary

 0 Introduction.
 1 First Principles.
 2 Further Properties of Locally Nilpotent Derivations.
 3 Polynomial Rings.
 4 Dimension Two.
 5 Dimension Three.
 6 Linear Actions of Vector Groups.
 7 NonFinitely Generated Kernels.
 8 Algorithms.
 9 The MakarLimanov and Derksen Invariants.
 10 Slices, Embeddings and Cancellation.
 11 Epilogue. References. Index.
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QA564 .F75 2006  Available 
 Freudenburg, Gene.
 Berlin : SpringerVerlag, c2006.
 Description
 Book — xi, 261 p. : ill.
11. Linear algebraic monoids [2005]
 Renner, Lex Ellery, 1952
 Berlin ; New York : Springer, c2005.
 Description
 Book — xii, 246 p. : ill. ; 24 cm.
 Summary

 Introduction. Background. Algebraic Monoids. Regularity Conditions. Classification of Reductive Monoids. Universal Constructions. Orbit Structure of Reductive Monoids. The Monoid Analogue of the Bruhat Decomposition. Representations and Blocks of Algebraic Monoids. Monoids of Lie Type. Cell Decomposition of Algebraic Monoids. Conjugacy Classes. The Centralizer of a Semisimple Element. Combinatorics Related to Algebraic Monoids. Related Developments. References. Index.
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QA169 .R46 2005  Available 
12. Multiplicative invariant theory [2005]
 Lorenz, Martin, 1951
 Berlin : Springer, c2005.
 Description
 Book — xi, 177 p. : ill. ; 24 cm.
 Summary

 Introduction. Notations and Conventions. List of Abbreviations and Symbols. Groups Acting on Lattices. Permutation Lattices and Flasque Equivalence. Multiplicative Actions. Class Group. Picard Group. Multiplicative Invariants of Reflection Groups. Regularity. The CohenMacaulay Property. Multiplicative Invariant Fields. Problems. References.
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QA201 .L67 2005  Available 
13. Projective duality and homogeneous spaces [2005]
 Tevelev, E. A. (Evgueni A.)
 Berlin ; New York : Springer, c2005.
 Description
 Book — xiv, 250 p. : ill. ; 25 cm.
 Summary

 Introduction to Projective Duality. Actions with Finitely Many Orbits. Local Calculations. Projective Constructions. Vector Bundles Methods. Degree of the Dual Variety. Varieties with Positive Defect. Dual Varieties of Homogeneous Spaces. SelfDual Varieties. Singularities of Dual Varieties. References. Index.
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QA471 .T48 2005  Available 
 Tevelev, E. A. (Evgueni A.)
 Berlin ; New York : Springer, c2005.
 Description
 Book — xiv, 250 p. : ill.
 Berlin ; New York : Springer, 2004.
 Description
 Book — xii, 238 p. : ill. ; 24 cm.
 Summary

 Ciliberto, Di Gennaro: Factoriality of Certain Hypersurfaces of P^4 with Ordinary Double Points. Ciliberto, Di Gennaro: Boundness for Low Codimensional Subvarieties. De Concini: Normality and NonNormality of Certain Semigroups and Orbit Closures. Landsberg, Manivel: Representation Theory and Projective Geometry. Hwang, Mok: Deformation Rigidity of the 20Dimensional F_4Homogeneous Space Associated to a Short Root. Mukai: Geometric Realization of TShaped Root Systems and Counterexamples to Hilbert's Fourteenth Problem. Krashen, Saltman: SeveriBrauer Varieties and Symmetric Powers. Popov, Tevelev: SelfDual Algebraic Varieties and Nilpotent Orbits in Symmetric Pairs. Snow: The Role of Exotic Affine Spaces in the Classification of Homogeneous Affine Varieties. Tevelev: Hermitian Characteristics of Nilpotent Elements. Zak: Determinants of Projective Varieties and their Degrees.
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SAL3 (offcampus storage)
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QA564 .A44 2004  Available 
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