B bell, groups and representations, gtm 162, springer 1995 2. Galgebrasandmodularrepresentationjz556562020 adobe. We also study some aspects of covering homomorphisms and the green correspondence in this context cf. Oct 17, 2009 in this paper, we generalize the notion of cover relationship on modules over finite groups and blocks of modular group algebras to the case of local interior g algebras by the embedding method. Biset functors, saturated fusion systems, and modular. They are based on the first authors notes from a lecture series delivered by the second author at the simons centre for geometry and physics in august 2019. Galgebras and modular representation theory, oxford science publications, clarendon, oxford 1995. Boisen, the representation theory of fully groupgraded algebras, j. Finally, we will show how to use the representation theory. Our aim is to show some aspects of cohomology theory of finite groups concerning projectivity of modules relative to both subgroups and modules.
Ams transactions of the american mathematical society. Please read our short guide how to send a book to kindle. It provides accessible notes on some complex recent results and introduces the reader to an active area of research in pure mathematics. Our arguments in the modular case draw and expand upon shapovalovs. For the standard facts on the modular representation theory of. Its aim is to provide a comprehensive treatment of the theory of. Significant results have been obtained by means of this approach, which also sheds new light on modular representation.
A block refinement of the greenpuig correspondences in finite group modular representation theory, int. Its aim is to provide a comprehensive treatment of the theory of galgebras and to show how this theory is used to solve various problems in representation theory. In this chapter, we provide an extensive account of the theory of frobenius and symmetric algebras. Some remarks on the tensor product of algebras and. Galgebras and modular representation theory, clarendon press, oxford 1995. This places these results in the standard integral finite group modular representation theory of g algebras as pioneered by puig cf. Galgebras and modular representation theory, oxford university press, oxford, 1995. Thematic of didactic activities per weeks schedule of the courses and seminars week 1. As a byproduct of our investigations, we establish a number of important results pertaining to modular representation theory of groups and block theory of group algebras. Ams proceedings of the american mathematical society. On the socle of an endomorphism algebra on the socle of an endomorphism algebra hiss, gerhard. Representation theory princeton math princeton university. Thevenaz, galgebras and modular representation theory, oxford university press, 1995. Lectures on the geometry and modular representation theory.
On the cover relationship for local interior g algebras. This advanced text develops a new approach to the modular representation theory of finite groups. Let p be a sylow psubgroup of g, and assume that p has an order p. The modular representation theory of g over k is the module theory of the group ring. Galgebras and modular representation theory citeseerx. Derived categories and delignelusztig varieties ii annals. The modular representation theory of finite groups david a. Alperin, local representation theory, cambridge university press, 1986. We will also explain how the representation theory. To generalize this notion the theory of projectivity relative to modules was introduced by the first author. Galgebras and modular representation theory jacques. Galgebras and modular representation theory book, 1995.
Its aim is to provide a comprehensive treatment of the theory of g algebras and to show how this theory is used to solve various problems in representation theory. Gerstenhaber, theory of convex cones, in activity analysis of production and allocation t. General pattern theory jacques faraut and adam koranyi. In the context of galgebras, we prove that green correspondent points satisfy some important properties that are suggested by the classical finite group green correspondence. Our aim is to show some aspects of cohomology theory of finite groups concerning projectivity of modules relative to. Relative projectivity of modules and cohomology theory of. Automorphismes, graduations et categories triangulees.
B bell, groups and representations, gtm 162, springer 1995. Pages 3284 from volume 178 20, issue 1 by radha kessar, gunter malle. We study ungraded, commutative kalgebras r on which g acts by kalgebra automorphisms rendering r a projective kgmodule. In the context of g algebras, we prove that green correspondent points satisfy some important properties that are suggested by the classical finite group green correspondence.
Vertex operator algebras, number theory and related topics a. Let abe a ring and let f abe the category of all left amodules. Galgebras and modular representation theory hansjoachim baues. We describe how the decomposition matrix of a finite group with split bnpair, with respect to a nondescribing prime. Received july 26, 2010 accepted september 24, 2010 \babe. Coconet 10 symmetric algebras, skew category algebras and inverse semigroups, j. A representation of an algebra a also called a left amodule is a vector.
A remark on the green correspondence on galgebras algebra. Chapter 4 considers some of the myriad applications of modular representation theory to. Please put your name on every sheet of your manuscript. This book presents a new approach to the modular representation theory of a finite group g. The book provides a balanced and comprehensive account of the subject, detailing the methods needed to analyze representations that arise in many areas of mathematics. Some familiarity with the basics of representation theory of finite groups and finite dimensional associative algebras would be helpful. Galgebras and modular representation theory infoscience. A course in finite group representation theory by peter webb.
Linckelmann, transfer in hochschild cohomology of blocks of. The results are applied to the modular hecke algebra of a finite group with a cyclic. Suppose that r is an r0algebra which as an r0module is. Vertex operator algebras, number theory and related topics.
Throughout these notes, g denotes a group and k denotes a field. G algebras and modular representation theory, oxford science publications, clarendon, oxford 1995. In this paper, we generalize the notion of cover relationship on modules over finite groups and blocks of modular group algebras to the case of local interior galgebras by the embedding method. This places these results in the standard integral finite group modular representation theory of galgebras as pioneered by puig cf. Oxford university press, walton street, oxford ox2 6dp. We will consider the green correspondence, then use galgebras to unite the blocktheoretic and moduletheoretic approaches somewhat. In the sequel, we shall refer to the case of up resp. Galgebras, clifford theory, and the green correspondence. Marks may be deducted for excessive length of solutions. The representation theory of finite groups, northholland, amsterdam, 1982. Our arguments in the modular case draw and expand upon shapovalovs original paper s.
Galgebras and modular representation theory oxford. Thevenaz, g algebras and modular representation theory, clarendon press, oxford, 1995. In the modular representation theory of finite groups the theory of projectivity relative to subgroups is of fundamental importance. Received july 26, 2010 accepted september 24, 2010. Oct 19, 2004 in the modular representation theory of finite groups the theory of projectivity relative to subgroups is of fundamental importance. Gr 1 oct 2016 on cohomology of saturated fusion systems and support varieties constantincosmin todea department of mathematics, technical university of clujnapoca, str. Tensor product and local interior galgebras wenlin huang school of mathematical. Symmetric functions and hall polynomials 2nd edition b. Galgebrasand modular representation jz556562020 adobe acrobat reader dcdownload adobe acrobat reader dc ebook pdf.
Significant results have been obtained by means of this approach, which also sheds new light on modular representation theory. Biset functors, saturated fusion systems, and modular representation theory report 20 january 31, 2014 the collaboration of the french team, composed of serge bouc and radu stancu, and the romanian team, composed of andrei marcus and constantincosmin todea continued in 20 with the visit of the french team in cluj, during the second half of. May 25, 2011 automorphismes, graduations et categories triangulees volume 10 issue 3 raphael rouquier. Thevenaz, g algebras and modular representation theory, oup, 1994, chapter 1. Derived categories and delignelusztig varieties ii. Introduction to representation theory by pavel etingof. Shapovalov determinant for restricted and quantized. These notes provide a concise introduction to the representation theory of reductive algebraic groups in positive characteristic, with an emphasis on lusztigs character formula and geometric representation theory. Thevenaz, galgebras and modular representation theory, clarendon press, oxford, 1995. Work on documents anywhere using the acrobat reader mobile app its packed with all the tools you need to convert edit and sign pdfs you can use your device camera to capture a document whiteboard or receipt and save it as a pdf. Quasiisolated blocks and brauers height zero conjecture. Galgebras and modular representation theory pdf free.
Galgebras and modular representation theory jacques thevenaz download bok. A correction to a remark on the green correspondence on g. We get some properties on the embedding method and establish a relationship between the principal block correspondence and the cover relationship. Modular representation theory university of warwick.
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