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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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Communal living --- Fathers and daughters --- Girls --- Imagination --- Vie en communauté --- Pères et filles --- Filles --- Imagination --- Fiction --- Fiction --- Fiction --- Fiction --- Romans --- Romans, nouvelles, etc. --- Romans --- Romans --- New York (State) --- New York (Etat) --- Fiction --- Romans

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Although ideas from quantum physics play an important role in many parts of modern mathematics, there are few books about quantum mechanics aimed at mathematicians. This book introduces the main ideas of quantum mechanics in language familiar to mathematicians. Readers with little prior exposure to physics will enjoy the book's conversational tone as they delve into such topics as the Hilbert space approach to quantum theory; the Schrödinger equation in one space dimension; the Spectral Theorem for bounded and unbounded self-adjoint operators; the Stone–von Neumann Theorem; the Wentzel–Kramers–Brillouin approximation; the role of Lie groups and Lie algebras in quantum mechanics; and the path-integral approach to quantum mechanics. The numerous exercises at the end of each chapter make the book suitable for both graduate courses and independent study. Most of the text is accessible to graduate students in mathematics who have had a first course in real analysis, covering the basics of L2 spaces and Hilbert spaces.  The final chapters introduce readers who are familiar with the theory of manifolds to more advanced topics, including geometric quantization.

topologie (wiskunde) --- Quantum mechanics. Quantumfield theory --- Functional analysis --- Mathematical physics --- Mathematics --- Topological groups. Lie groups --- wiskunde --- quantumfysica --- functies (wiskunde) --- fysica --- Quanta, Teoría de los --- Quantum theory. --- Functional analysis. --- Topological Groups. --- Mathematical physics. --- Mathematical Physics. --- Mathematical Applications in the Physical Sciences. --- Quantum Physics. --- Functional Analysis. --- Topological Groups, Lie Groups. --- Mathematical Methods in Physics. --- Physical mathematics --- Physics --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Mechanics --- Thermodynamics --- Groups, Topological --- Continuous groups --- Quantum physics. --- Topological groups. --- Lie groups. --- Physics. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Quantum theory

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Evolution. Phylogeny --- General embryology. Developmental biology --- Developmental biology. --- Evolution (Biology) --- Evolution (Biology).

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Bones and Cartilage provides the most in-depth review ever assembled on the topic. It examines the function, development and evolution of bone and cartilage as tissues, organs and skeletal systems. It describes how bone and cartilage is developed in embryos and are maintained in adults, how bone reappears when we break a leg, or even regenerates when a newt grows a new limb, or a lizard a tail. This book also looks at the molecules and cells that make bones and cartilages and how they differ in various parts of the body and across species.

Bone. --- Bone. Bones--Physiology. Bones--Growth. . --- Bones. --- Bones - Growth. --- Bones - Physiology. --- Bone --- Bones --- Connective Tissue --- Musculoskeletal System --- Skeleton --- Musculoskeletal Physiological Processes --- Organogenesis --- Tissues --- Embryonic and Fetal Development --- Anatomy --- Musculoskeletal Physiological Phenomena --- Morphogenesis --- Musculoskeletal and Neural Physiological Phenomena --- Growth and Development --- Phenomena and Processes --- Physiological Processes --- Physiological Phenomena --- Osteogenesis --- Cartilage --- Bone Development --- Bone and Bones --- Musculoskeletal Development --- Human Anatomy & Physiology --- Health & Biological Sciences --- Physiology --- Growth --- Physiology. --- Growth. --- Bone development --- Bone growth --- Osteology --- Musculoskeletal system --- Calcification --- Connective tissues