By Li J., Su Y., Zhu L.
By Jürgen Fuchs, Christoph Schweigert
This is often an creation to Lie algebras and their purposes in physics. First illustrating how Lie algebras come up obviously from symmetries of actual structures, the ebook then offers a close creation to Lie algebras and their representations, overlaying the Cartan-Weyl foundation, basic and affine Lie algebras, genuine varieties and Lie teams, the Weyl team, automorphisms, loop algebras and maximum weight representations. The ebook additionally discusses particular extra issues, reminiscent of Verma modules, Casimirs, tensor items and Clebsch-Gordan coefficients, invariant tensors, subalgebras and branching principles, younger tableaux, spinors, Clifford algebras and supersymmetry, representations on functionality areas, and Hopf algebras and illustration jewelry. a close reference checklist is supplied, and lots of workouts and examples through the booklet illustrate using Lie algebras in actual actual difficulties. The textual content is written at a degree obtainable to graduate scholars, yet also will supply a complete reference for researchers.
By Manfred Stern
Lattice thought advanced as a part of algebra within the 19th century during the paintings of Boole, Peirce and Schröder, and within the first 1/2 the 20 th century in the course of the paintings of Dedekind, Birkhoff, Ore, von Neumann, Mac Lane, Wilcox, Dilworth, and others. In Semimodular Lattices, Manfred Stern makes use of successive generalizations of distributive and modular lattices to stipulate the advance of semimodular lattices from Boolean algebras. He makes a speciality of the real concept of semimodularity, its many ramifications, and its functions in discrete arithmetic, combinatorics, and algebra. the writer surveys and analyzes Birkhoff's idea of semimodularity and a number of the comparable thoughts in lattice idea, and he provides theoretical effects in addition to functions in discrete arithmetic crew idea and common algebra. detailed emphasis is given to the combinatorial features of finite semimodular lattices and to the connections among matroids and geometric lattices, antimatroids and in the neighborhood distributive lattices. The e-book additionally offers with lattices which are "close" to semimodularity or should be mixed with semimodularity, for instance supersolvable, admissible, constant, robust, and balanced lattices. Researchers in lattice conception, discrete arithmetic, combinatorics, and algebra will locate this publication invaluable.