By Brian Hall
Newly formatted for Kindle, this textbook treats Lie teams, Lie algebras and their representations in an effortless yet totally rigorous model requiring minimum must haves. particularly, the speculation of matrix Lie teams and their Lie algebras is constructed utilizing in basic terms linear algebra, and extra motivation and instinct for proofs is equipped than in such a lot vintage texts at the subject.
In addition to its obtainable therapy of the fundamental concept of Lie teams and Lie algebras, the publication is usually noteworthy for including:
- a remedy of the Baker–Campbell–Hausdorff formulation and its use rather than the Frobenius theorem to set up deeper effects in regards to the courting among Lie teams and Lie algebras
- motivation for the equipment of roots, weights and the Weyl team through a concrete and specified exposition of the illustration conception of sl(3;C)
- an unconventional definition of semisimplicity that enables for a quick improvement of the constitution idea of semisimple Lie algebras
- a self-contained development of the representations of compact teams, self reliant of Lie-algebraic arguments
The moment variation of Lie teams, Lie Algebras, and Representations comprises many colossal advancements and additions, between them: a wholly new half dedicated to the constitution and illustration concept of compact Lie teams; an entire derivation of the most homes of root platforms; the development of finite-dimensional representations of semisimple Lie algebras has been elaborated; a remedy of common enveloping algebras, together with an evidence of the Poincaré–Birkhoff–Witt theorem and the lifestyles of Verma modules; whole proofs of the Weyl personality formulation, the Weyl size formulation and the Kostant multiplicity formula.
Review of the 1st edition:
This is a wonderful ebook. It merits to, and surely will, turn into the traditional textual content for early graduate classes in Lie crew concept ... a major addition to the textbook literature ... it truly is hugely recommended.
— The Mathematical Gazette
By Norman L. Biggs,A. T. White
By Yi-Zhi Huang
By Marcus du Sautoy,Luke Woodward
Zeta services were a strong instrument in arithmetic during the last centuries. This publication considers a brand new classification of non-commutative zeta services which encode the constitution of the subgroup lattice in limitless teams. It explores the analytic habit of those services including an research of sensible equations. The booklet examines many vital examples of zeta capabilities, offering a huge database of specific examples and techniques for calculation.
By Shahn Majid
By Yakov Berkovich,Zvonimir Janko
This is the second one of 3 volumes dedicated to trouble-free finite p-group concept. just like the 1st quantity, hundreds and hundreds of significant effects are analyzed and, in lots of situations, simplified. vital subject matters awarded during this monograph contain: (a) class of p-groups all of whose cyclic subgroups of composite orders are common, (b) type of 2-groups with precisely 3 involutions, (c) proofs of Ward's theorem on quaternion-free teams, (d) 2-groups with small centralizers of an involution, (e) category of 2-groups with precisely 4 cyclic subgroups of order 2n > 2, (f) new proofs of Blackburn's theorem on minimum nonmetacyclic teams, (g) class of p-groups all of whose subgroups of index p2 are abelian, (h) category of 2-groups all of whose minimum nonabelian subgroups have order eight, (i) p-groups with cyclic subgroups of index p2 are classified.
This quantity comprises hundreds of thousands of unique workouts (with all tricky routines being solved) and a longer checklist of approximately seven-hundred open difficulties. The publication relies on quantity 1, and it really is appropriate for researchers and graduate scholars of arithmetic with a modest historical past on algebra.
By Jean-Philippe Anker,Bent Orsted
* First of 3 self sufficient, self-contained volumes less than the overall identify, "Lie Theory," that includes unique effects and survey paintings from well known mathematicians.
* includes J. C. Jantzen's "Nilpotent Orbits in illustration Theory," and K.-H. Neeb's "Infinite Dimensional teams and their Representations."
* complete remedies of the appropriate geometry of orbits in Lie algebras, or their duals, and the correspondence to representations.
* may still gain graduate scholars and researchers in arithmetic and mathematical physics.
By Julio R. Bastida,Roger Lyndon
By Igor Frenkel,James Lepowsky,Arne Meurman
By Stephanie Frank Singer