Solid but concise, this account of Lie algebra emphasizes the theory's simplicity and offers new approaches to major theorems. Author David J. Winter, a Professor of Mathematics at the University of Michigan, also presents a general, extensive treatment of Cartan and related Lie subalgebras over arbitrary fields.Preliminary material covers modules and nonassociate algebras, followed by a compact, self-contained development of the theory of Lie algebras of characteristic 0. Topics include solvable and nilpotent Lie algebras, Cartan subalgebras, and Levi's radical splitting theorem and the complete reducibility of representations of semisimple Lie algebras. Additional subjects include the isomorphism theorem for semisimple Lie algebras and their irreducible modules, automorphism of Lie algebras, and the conjugacy of Cartan subalgebras and Borel subalgebras. An extensive theory of Cartan and related subalgebras of Lie algebras over arbitrary fields is developed in the final chapter, and an appendix offers background on the Zariski topology.

Abstract Lie Algebras (Dover Books on Mathematics)

Science & Math

David J Winter

Mathematics

Dover Publications

The theft of a religious relic has the village of Durum in an ethical quandary. The theft has also caused trouble within the monastery, the nunnery and St Anne's church located in the village. The interaction among the brothers and sisters at Durum monastery and nunnery and those charged with overseeing Durum takes these men and women on a journey to and from the towns and villages of the Frankish Kingdom to the center of spiritual power in Rome. The adventure concludes as Charlemagne and Pope Leo III make history on Christmas Day 800 AD.

Turning North

Literature & Fiction

Literary

Aberdeen Bay

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Books by David J Winter