Titlebook: Symmetry, Representations, and Invariants; Roe Goodman,Nolan R. Wallach Textbook 2009 Springer-Verlag New York 2009 Abstract algebra.Group

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0072-5285 ions, and Invariants.: (1) Early chapters suitable for honors undergraduate or beginning graduate courses, requiring only linear algebra, basic abstract algebra, and advanced calculus; (2) Applications to geome978-1-4419-2729-3978-0-387-79852-3Series ISSN 0072-5285 Series E-ISSN 2197-5612

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Structure of Classical Groups,he root spaces are encoded by the set of roots; we use this information to prove that the classical (trace-zero) Lie algebras are simple (or semisimple). In the final section of the chapter we develop some general Lie algebra methods (solvable Lie algebras, Killing form) and show that every semisimp

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Classical Invariant Theory,we first find all polynomial invariants of at most dim . vectors. We then use this special case to transform the general problem of tensor invariants for an arbitrary number of vectors into an invariant problem for .(.) of the type we have already solved..The FFT furnishes generators for the commuta

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Representations on Spaces of Regular Functions,f a symmetric space. This chapter is also less self-contained than the earlier ones. For example, the basic results of Chevalley on invariants corresponding to symmetric pairs are only quoted (although for the pairs of classical type these facts are verified on a case-by-case basis). We also mix alg

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Textbook 2009 complete arguments now given in the general case...Key Features of .Symmetry, Representations, and Invariants.: (1) Early chapters suitable for honors undergraduate or beginning graduate courses, requiring only linear algebra, basic abstract algebra, and advanced calculus; (2) Applications to geome

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ase study sample, which includes 5 community-led projects and 5 small or medium enterprises, based on aquaponic or hydroponic technologies. 2 of these projects were closed during the drafting of the book. However, they were included in order to document the vulnerability of small-scale initiatives,

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