Lie Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lie Groups write by Claudio Procesi. This book was released on 2007-10-17. Lie Groups available in PDF, EPUB and Kindle. Lie groups has been an increasing area of focus and rich research since the middle of the 20th century. In Lie Groups: An Approach through Invariants and Representations, the author's masterful approach gives the reader a comprehensive treatment of the classical Lie groups along with an extensive introduction to a wide range of topics associated with Lie groups: symmetric functions, theory of algebraic forms, Lie algebras, tensor algebra and symmetry, semisimple Lie algebras, algebraic groups, group representations, invariants, Hilbert theory, and binary forms with fields ranging from pure algebra to functional analysis. By covering sufficient background material, the book is made accessible to a reader with a relatively modest mathematical background. Historical information, examples, exercises are all woven into the text. This unique exposition is suitable for a broad audience, including advanced undergraduates, graduates, mathematicians in a variety of areas from pure algebra to functional analysis and mathematical physics.
Reflection Groups and Invariant Theory
Reflection Groups and Invariant Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Reflection Groups and Invariant Theory write by Richard Kane. This book was released on 2013-03-09. Reflection Groups and Invariant Theory available in PDF, EPUB and Kindle. Reflection groups and invariant theory is a branch of mathematics that lies at the intersection between geometry and algebra. The book contains a deep and elegant theory, evolved from various graduate courses given by the author over the past 10 years.
Symmetry, Representations, and Invariants
Symmetry, Representations, and Invariants - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Symmetry, Representations, and Invariants write by Roe Goodman. This book was released on 2009-07-30. Symmetry, Representations, and Invariants available in PDF, EPUB and Kindle. Symmetry is a key ingredient in many mathematical, physical, and biological theories. Using representation theory and invariant theory to analyze the symmetries that arise from group actions, and with strong emphasis on the geometry and basic theory of Lie groups and Lie algebras, Symmetry, Representations, and Invariants is a significant reworking of an earlier highly-acclaimed work by the authors. The result is a comprehensive introduction to Lie theory, representation theory, invariant theory, and algebraic groups, in a new presentation that is more accessible to students and includes a broader range of applications. The philosophy of the earlier book is retained, i.e., presenting the principal theorems of representation theory for the classical matrix groups as motivation for the general theory of reductive groups. The wealth of examples and discussion prepares the reader for the 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 geometry (curvature tensors), topology (Jones polynomial via symmetry), and combinatorics (symmetric group and Young tableaux); (3) Self-contained chapters, appendices, comprehensive bibliography; (4) More than 350 exercises (most with detailed hints for solutions) further explore main concepts; (5) Serves as an excellent main text for a one-year course in Lie group theory; (6) Benefits physicists as well as mathematicians as a reference work.
An Introduction to Lie Groups and Lie Algebras
An Introduction to Lie Groups and Lie Algebras - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Introduction to Lie Groups and Lie Algebras write by Alexander A. Kirillov. This book was released on 2008-07-31. An Introduction to Lie Groups and Lie Algebras available in PDF, EPUB and Kindle. This book is an introduction to semisimple Lie algebras. It is concise and informal, with numerous exercises and examples.
Lie Groups, Lie Algebras, and Representations
Lie Groups, Lie Algebras, and Representations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lie Groups, Lie Algebras, and Representations write by Brian Hall. This book was released on 2015-05-11. Lie Groups, Lie Algebras, and Representations available in PDF, EPUB and Kindle. This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites. In particular, the theory of matrix Lie groups and their Lie algebras is developed using only linear algebra, and more motivation and intuition for proofs is provided than in most classic texts on the subject. In addition to its accessible treatment of the basic theory of Lie groups and Lie algebras, the book is also noteworthy for including: a treatment of the Baker–Campbell–Hausdorff formula and its use in place of the Frobenius theorem to establish deeper results about the relationship between Lie groups and Lie algebras motivation for the machinery of roots, weights and the Weyl group via a concrete and detailed exposition of the representation theory of sl(3;C) an unconventional definition of semisimplicity that allows for a rapid development of the structure theory of semisimple Lie algebras a self-contained construction of the representations of compact groups, independent of Lie-algebraic arguments The second edition of Lie Groups, Lie Algebras, and Representations contains many substantial improvements and additions, among them: an entirely new part devoted to the structure and representation theory of compact Lie groups; a complete derivation of the main properties of root systems; the construction of finite-dimensional representations of semisimple Lie algebras has been elaborated; a treatment of universal enveloping algebras, including a proof of the Poincaré–Birkhoff–Witt theorem and the existence of Verma modules; complete proofs of the Weyl character formula, the Weyl dimension formula and the Kostant multiplicity formula. Review of the first edition: This is an excellent book. It deserves to, and undoubtedly will, become the standard text for early graduate courses in Lie group theory ... an important addition to the textbook literature ... it is highly recommended. — The Mathematical Gazette
