By Jean-Pierre Serre
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During this booklet, 3 authors introduce readers to robust approximation tools, analytic pro-p teams and zeta services of teams. each one bankruptcy illustrates connections among countless staff idea, quantity concept and Lie conception. the 1st introduces the idea of compact p-adic Lie teams. the second one explains how equipment from linear algebraic teams may be utilised to review the finite photographs of linear teams.
This precise textual content is an creation to harmonic research at the least difficult symmetric areas, particularly Euclidean area, the field, and the Poincaré higher part plane. This booklet is meant for starting graduate scholars in arithmetic or researchers in physics or engineering. Written with an off-the-cuff sort, the publication locations an emphasis on motivation, concrete examples, heritage, and, certainly, functions in arithmetic, facts, physics, and engineering.
Influenced by means of the significance of the Campbell, Baker, Hausdorff, Dynkin Theorem in lots of diversified branches of arithmetic and Physics (Lie group-Lie algebra conception, linear PDEs, Quantum and Statistical Mechanics, Numerical research, Theoretical Physics, keep watch over thought, sub-Riemannian Geometry), this monograph is meant to: fully allow readers (graduates or experts, mathematicians, physicists or utilized scientists, accustomed to Algebra or no longer) to appreciate and observe the statements and various corollaries of the most result, provide a large spectrum of proofs from the fashionable literature, evaluating various strategies and furnishing a unifying standpoint and notation, offer a radical ancient history of the consequences, including unknown proof concerning the potent early contributions by means of Schur, Poincaré, Pascal, Campbell, Baker, Hausdorff and Dynkin, give an outlook at the functions, particularly in Differential Geometry (Lie staff concept) and research (PDEs of subelliptic variety) and quickly allow the reader, via an outline of the state-of-art and open difficulties, to appreciate the trendy literature relating a theorem which, notwithstanding having its roots before everything of the 20th century, has now not ceased to supply new difficulties and functions.
This graduate-level textual content offers an intensive grounding within the illustration conception of finite teams over fields and earrings. The e-book offers a balanced and finished account of the topic, detailing the equipment had to research representations that come up in lots of components of arithmetic. Key themes comprise the development and use of personality tables, the function of induction and limit, projective and straightforward modules for staff algebras, indecomposable representations, Brauer characters, and block idea.
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