Groups, Generators, Syzygies, and Orbits in Invariant TheoryAmerican Mathematical Soc., 5 янв. 2011 г. - Всего страниц: 245 The history of invariant theory spans nearly a century and a half, with roots in certain problems from number theory, algebra, and geometry appearing in the work of Gauss, Jacobi, Eisenstein, and Hermite. Although the connection between invariants and orbits was essentially discovered in the work of Aronhold and Boole, a clear understanding of this connection had not been achieved until recently, when invariant theory was in fact subsumed by a general theory of algebraic groups. Written by one of the major leaders in the field, this book provides an excellent, comprehensive exposition of invariant theory. Its point of view is unique in that it combines both modern and classical approaches to the subject. The introductory chapter sets the historical stage for the subject, helping to make the book accessible to nonspecialists. |
Содержание
1 | |
Notation and Terminology | 19 |
Constructive Invariant Theory | 29 |
The Degree of the Poincare Series of the Algebra | 43 |
Syzygies in Invariant Theory | 61 |
Representations with Free Modules of Covariants | 127 |
A Classification of Normal Afline Quasihomogeneous | 147 |
Quasihomogeneous Curves Surfaces and Solids | 167 |
Appendix | 201 |
231 | |
243 | |
Другие издания - Просмотреть все
Groups, Generators, Syzygies, and Orbits in Invariant Theory Vladimir Leonidovich Popov Недоступно для просмотра - 1992 |
Groups, Generators, Syzygies, and Orbits in Invariant Theory V. L. Popov Недоступно для просмотра - 2011 |
Часто встречающиеся слова и выражения
action of G affine afline algebra k[V]G algebra of invariants algebraic group algebraic variety assertion assume automorphism AutX Borel subgroup Chapter classification coefficients connected semisimple group consider contains conv W(a COROLLARY corresponding curve cyclic group deduce defined definition denote elements embedding English transl equal equidimensional exists fiber field find finite finite group finite-dimensional first fix fixed point free algebra free modules functions fundamental weights G-modules GL(V group G hdk[V]G Hence Hilbert’s inequality integer invariant theory isomorphic Lemma Let G Lie algebra linear maximal torus minimal system module of covariants morphism NG(T noneffectivity kernel nontrivial nonzero normal notation obtain one-dimensional torus Poincare series polynomial problem PROOF properties Proposition quasihomogeneous varieties R(co R(wl R(wz rational reductive group resp respect S-variety satisfied semigroup semisimple group simple groups stabilizer subalgebra subgroup of G submodule subspace Suppose system of homogeneous Theorem Theorem 4.1 three-dimensional unipotent subgroup vector zero ZG(T zonohedron