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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.

Mathematics. --- Topological Groups, Lie Groups. --- Non-associative Rings and Algebras. --- Manifolds and Cell Complexes (incl. Diff.Topology). --- Algebra. --- Topological Groups. --- Cell aggregation --- Mathématiques --- Algèbre --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Calculus --- Nonassociative rings. --- Rings (Algebra). --- Topological groups. --- Lie groups. --- Manifolds (Mathematics). --- Complex manifolds. --- Aggregation, Cell --- Cell patterning --- Cell interaction --- Microbial aggregation --- Mathematical analysis --- Groups, Topological --- Continuous groups --- Representations of Lie groups. --- Representations of Lie algebras. --- Lie algebras. --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Analytic spaces --- Manifolds (Mathematics) --- Geometry, Differential --- Topology --- Algebraic rings --- Ring theory --- Algebraic fields --- Rings (Algebra) --- Lie groups --- Representations of Lie algebras --- Representations of Lie groups --- Cell aggregation_xMathematics --- Topological Groups --- Complex manifolds --- Nonassociative rings --- Electronic books

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To facilitate a deeper understanding of tensegrity structures, this book focuses on their two key design problems: self-equilibrium analysis and stability investigation. In particular, high symmetry properties of the structures are extensively utilized. Conditions for self-equilibrium as well as super-stability of tensegrity structures are presented in detail. An analytical method and an efficient numerical method are given for self-equilibrium analysis of tensegrity structures: the analytical method deals with symmetric structures and the numerical method guarantees super-stability. Utilizing group representation theory, the text further provides analytical super-stability conditions for the structures that are of dihedral as well as tetrahedral symmetry. This book not only serves as a reference for engineers and scientists but is also a useful source for upper-level undergraduate and graduate students. Keeping this objective in mind, the presentation of the book is self-contained and detailed, with an abundance of figures and examples.

Engineering. --- Structural Mechanics. --- Manifolds and Cell Complexes (incl. Diff.Topology). --- Engineering Design. --- Interior Architecture. --- Nonlinear Dynamics. --- Mechanics. --- Cell aggregation --- Mechanical engineering. --- Engineering design. --- Ingénierie --- Mécanique --- Génie mécanique --- Conception technique --- Mathematics. --- Cell aggregation_xMathematics. --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Civil Engineering --- Design, Engineering --- Engineering --- Engineering, Mechanical --- Classical mechanics --- Newtonian mechanics --- Aggregation, Cell --- Cell patterning --- Design --- Manifolds (Mathematics). --- Complex manifolds. --- Statistical physics. --- Structural mechanics. --- Industrial design --- Strains and stresses --- Physics --- Dynamics --- Quantum theory --- Machinery --- Steam engineering --- Cell interaction --- Microbial aggregation --- Mechanics, Applied. --- Solid Mechanics. --- Interior Architecture and Design. --- Applications of Nonlinear Dynamics and Chaos Theory. --- Classical Mechanics. --- Applied mechanics --- Engineering mathematics --- Interior architecture. --- Interiors. --- Mathematical statistics --- Architectural interiors --- Architecture, Interior --- Interior space (Architecture) --- Interiors --- Space (Architecture) --- Analytic spaces --- Manifolds (Mathematics) --- Geometry, Differential --- Topology --- Statistical methods