{"product_id":"classification-and-structure-theory-of-hasan-gundogan-9783832530242","title":"Classification and Structure Theory of Lie Algebras of Smooth Sections","description":"Lie groups and their \"derived objects\", Lie algebras, appear in various fields of mathematics and physics. At least since the beginning of the 20th century, and after the famous works of Wilhelm Killing, Elie Cartan, Eugenio Elia Levi, Anatoly Malcev and Igor Ado on the structure of finite-dimensional Lie algebras, the classification and structure theory of infinite-dimensional Lie algebras has become an interesting and fairly vast field of interest. This dissertation focusses on the structure of Lie algebras of smooth and k-times differentiable sections of finite-dimensional Lie algebra bundles, which are generalizations of the famous and well-understood affine Kac-Moody algebras. Besides answering the immediate structural questions (center, commutator algebra, derivations, centroid, automorphism group), this work approaches a classification of section algebras by homotopy theory. Furthermore, we determine a universal invariant symmetric bilinear form on Lie algebras of smooth sections and use this form to define a natural central extension which is universal, at least in the case of Lie algebra bundles with compact base manifold.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Hasan Gundogan\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 383253024X\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9783832530242\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Logos Verlag Berlin\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 01\/28\/2011\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 175\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback","brand":"Hasan Gundogan","offers":[{"title":"Paperback","offer_id":48450126348543,"sku":"9783832530242","price":54.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_18f0dfda-d1db-42bf-b5ea-b8cdc9922dc3.jpg?v=1777266325","url":"https:\/\/www.whiterainbookhouse.com\/products\/classification-and-structure-theory-of-hasan-gundogan-9783832530242","provider":"WR Book House","version":"1.0","type":"link"}