Publisher: Springer; 1st ed. 2015 edition (December 31, 2015)
Format: PDF / Kindle / ePub
Size: 9.5 MB
Downloadable formats: PDF
In sleek arithmetic, a Lie staff potential a gaggle that's additionally a manifold. whereas Lie teams are geometric items, Lie algebras are algebraic parts that represent the infinitesimal constitution of Lie teams. The theories of Lie teams and Lie algebras originated within the overdue 19th century and these days they include an necessary a part of sleek arithmetic connecting just about all of its sub-disciplines. This publication, written via one of many prime specialists within the box, goals to supply a pedagogical advent to crucial thoughts and strategies within the theories of Lie teams and their representations in a fashion understandable to a large viewers in arithmetic and mathematical physics. The booklet starts with an hassle-free creation to the constitution of topological teams, their illustration conception and Fourier research, by way of an in depth account of the Peter–Weyl theorem for compact teams. the second one 1/2 the booklet begins with the class conception of finite dimensional irreducible representations and leads the reader to the Cartan–Weyl optimum weight idea, together with ample enlightening examples of classical matrix teams. a different function of the publication is the ultimate chapters devoted to the limitless dimensional unitary illustration thought and the Borel–Weil idea, for which no introductory textbook exists but. The author’s writing kind is such that every time an summary idea is brought, he attempts to encourage the reader ahead of giving a proper definition. certain efforts are made to carry these strategies and ideas to mild which are frequently hidden at the back of theorems; each clarification is definitely notion out to reduce the heritage wisdom had to are aware of it; routines are connected on the finish of every bankruptcy with totally worked-out recommendations to assist readers attempt their realizing. those beneficial properties together make this ebook a valuable source for either scholars and researchers accomplishing this quickly turning out to be box of study.