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| Author | : Rebecca Waldecker |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 164 |
| Release | : 2013-10-23 |
| Genre | : Mathematics |
| ISBN | : 082188803X |
This text provides a new proof of Glauberman's Z*-Theorem under the additional hypothesis that the simple groups involved in the centraliser of an isolated involution are known simple groups.
| Author | : David A. Craven |
| Publisher | : Springer Nature |
| Total Pages | : 294 |
| Release | : 2019-08-30 |
| Genre | : Mathematics |
| ISBN | : 3030217922 |
This book provides an accessible introduction to the state of the art of representation theory of finite groups. Starting from a basic level that is summarized at the start, the book proceeds to cover topics of current research interest, including open problems and conjectures. The central themes of the book are block theory and module theory of group representations, which are comprehensively surveyed with a full bibliography. The individual chapters cover a range of topics within the subject, from blocks with cyclic defect groups to representations of symmetric groups. Assuming only modest background knowledge at the level of a first graduate course in algebra, this guidebook, intended for students taking first steps in the field, will also provide a reference for more experienced researchers. Although no proofs are included, end-of-chapter exercises make it suitable for student seminars.
| Author | : Florica C. Cîrstea |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 97 |
| Release | : 2014-01-08 |
| Genre | : Mathematics |
| ISBN | : 0821890220 |
In particular, for b = 1 and λ = 0, we find a sharp condition on h such that the origin is a removable singularity for all non-negative solutions of [[eqref]]one, thus addressing an open question of Vázquez and Véron.
| Author | : |
| Publisher | : Elsevier |
| Total Pages | : 209 |
| Release | : 2000-04-01 |
| Genre | : Mathematics |
| ISBN | : 9780080954134 |
Locally Finite Groups
| Author | : Stephen D. Smith |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 231 |
| Release | : 2018-04-30 |
| Genre | : Finite simple groups |
| ISBN | : 1470442914 |
Classification of Finite Simple Groups (CFSG) is a major project involving work by hundreds of researchers. The work was largely completed by about 1983, although final publication of the “quasithin” part was delayed until 2004. Since the 1980s, CFSG has had a huge influence on work in finite group theory and in many adjacent fields of mathematics. This book attempts to survey and sample a number of such topics from the very large and increasingly active research area of applications of CFSG. The book is based on the author's lectures at the September 2015 Venice Summer School on Finite Groups. With about 50 exercises from original lectures, it can serve as a second-year graduate course for students who have had first-year graduate algebra. It may be of particular interest to students looking for a dissertation topic around group theory. It can also be useful as an introduction and basic reference; in addition, it indicates fuller citations to the appropriate literature for readers who wish to go on to more detailed sources.
| Author | : Milen Yakimov |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 104 |
| Release | : 2014-04-07 |
| Genre | : Mathematics |
| ISBN | : 082189174X |
Joseph and Hodges-Levasseur (in the A case) described the spectra of all quantum function algebras on simple algebraic groups in terms of the centers of certain localizations of quotients of by torus invariant prime ideals, or equivalently in terms of orbits of finite groups. These centers were only known up to finite extensions. The author determines the centers explicitly under the general conditions that the deformation parameter is not a root of unity and without any restriction on the characteristic of the ground field. From it he deduces a more explicit description of all prime ideals of than the previously known ones and an explicit parametrization of .
| Author | : Christopher P. Bendel |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 110 |
| Release | : 2014-04-07 |
| Genre | : Mathematics |
| ISBN | : 0821891758 |
In general, little is known about the representation theory of quantum groups (resp., algebraic groups) when l (resp., p ) is smaller than the Coxeter number h of the underlying root system. For example, Lusztig's conjecture concerning the characters of the rational irreducible G -modules stipulates that p=h. The main result in this paper provides a surprisingly uniform answer for the cohomology algebra H (u ? ,C) of the small quantum group.
| Author | : Mark Green |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 158 |
| Release | : 2014-08-12 |
| Genre | : Mathematics |
| ISBN | : 0821898574 |
The authors study the complex geometry and coherent cohomology of nonclassical Mumford-Tate domains and their quotients by discrete groups. Their focus throughout is on the domains which occur as open -orbits in the flag varieties for and , regarded as classifying spaces for Hodge structures of weight three. In the context provided by these basic examples, the authors formulate and illustrate the general method by which correspondence spaces give rise to Penrose transforms between the cohomologies of distinct such orbits with coefficients in homogeneous line bundles.
| Author | : Daniel Gorenstein |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 339 |
| Release | : 2013-11-27 |
| Genre | : Mathematics |
| ISBN | : 1468484974 |
In February 1981, the classification of the finite simple groups (Dl)* was completed,t. * representing one of the most remarkable achievements in the history or mathematics. Involving the combined efforts of several hundred mathematicians from around the world over a period of 30 years, the full proof covered something between 5,000 and 10,000 journal pages, spread over 300 to 500 individual papers. The single result that, more than any other, opened up the field and foreshadowed the vastness of the full classification proof was the celebrated theorem of Walter Feit and John Thompson in 1962, which stated that every finite group of odd order (D2) is solvable (D3)-a statement expressi ble in a single line, yet its proof required a full 255-page issue of the Pacific 10urnal of Mathematics [93]. Soon thereafter, in 1965, came the first new sporadic simple group in over 100 years, the Zvonimir Janko group 1 , to further stimulate the 1 'To make the book as self-contained as possible. we are including definitions of various terms as they occur in the text. However. in order not to disrupt the continuity of the discussion. we have placed them at the end of the Introduction. We denote these definitions by (DI). (D2), (D3). etc.
| Author | : Vin de Silva |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 126 |
| Release | : 2014-06-05 |
| Genre | : Mathematics |
| ISBN | : 0821898868 |
The authors define combinatorial Floer homology of a transverse pair of noncontractible nonisotopic embedded loops in an oriented -manifold without boundary, prove that it is invariant under isotopy, and prove that it is isomorphic to the original Lagrangian Floer homology. Their proof uses a formula for the Viterbo-Maslov index for a smooth lune in a -manifold.
