پديد آورنده :
قمرشوشتري، رضا
عنوان :
توسيع هاي هم - جبري و هم-توسيع هاي جبري گالوايي
مقطع تحصيلي :
كارشناسي ارشد
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان: دانشكده علوم رياضي
يادداشت :
ص.ع به: فارسي و انگليسي
استاد راهنما :
محمود بهبودي، بهرام رنگي پور
استاد مشاور :
محمدرضا ودادي
توصيفگر ها :
نگاشت به هم پيچنده , ساختار به هم پيچيده , كلاف اساسي هم -جبري , كلاف اساسي دو گان
تاريخ نمايه سازي :
18/8/1388
استاد داور :
حسين خبازيان، عاطفه قرباني
تاريخ ورود اطلاعات :
1396/09/20
چكيده فارسي :
به فارسي و انگليسي : قابل رويت در نسخه ديجيتال
چكيده انگليسي :
Coalgebra Extensions and Algebra Coextensions of Galois Type Reza Ghamar Shoushtari r ghamarshoushtari@math iut ac ir August 12 2009 Master of Science Thesis in Farsi Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 IranSupervisors Dr Mahmood Behboodi mbehbood@cc iut ac ir and Dr Bahram Rangipour Univer sity of New Brunswick Canada bahram@unb ca 2000 MSC 16W30 17B37 81R50Key words coalgebra Galois extension algebra Galois coextension entwining map entwined structure coal gebra principle bundle dual principle bundle Abstract In this thesis we present an expanded account of coalgebra extensions and algebra coex tensions of Galois type based on article by Tomasz Brzezinski and Piotr M Hajac 1999 Let k be a eld C a coalgebra with structure map A a k algebra and a right C comodulewith structure map A and B b A A ba b A a a A Then B is called thesubalgebra of right coinvariants and A is called a right coalgebra Galois extension of B ifand only if the left A module right C comodule map m C A B A A B A A Cis bijective where m is the multiplication map of A and C and A mean the identity map of Cand A respectively This generalizes the notion of a Hopf Galois extension Let be a k linearmap C A A C such that C m m C A A C C A C C A A A where and are the unit and counit maps of A and C respectively Then C and A are saidto be entwined by and the triple A C is called an entwining structure It is shown thatif A be a coalgebra Galois extension of B Then there exists a unique map C A A C Centwining C with A and such that A MA with the structure maps m and A where CMA is the category of right A C modules whose objects are right A modules and rightC comodules V such that for all v V and a A V va v 0 v 1 a and morphismsare right A module right C comodule maps Moreover the dual notion of a coalgebra Galoisextension is de ned and the analogous results are also derived Also the notion of coalgebra principle bundle is introduced as a generalization of quantumgroup principle bundle Let A C be an entwining structure and let e C be a group likeelement Then B b A e b b e is a subalgebra of A and A B C e is calleda coalgebra principle bundle if and only if the map can A B A A C a a a e a is bijective It is shown that the concept of coalgebra principle bundle is related tothe concept of coalgebra galois extension Let A C be an entwining structure and e Cbe a group like element Then A B C e is a coalgebra principle bundle if and only ifthere exists a unique coaction A A A C such that A is a coalgebra Galois extentionof B by C is the canonical entwining map and A 1 1 e In addition the dual notionof coalgebra galois extension is de ned and the same result is also derived 1
استاد راهنما :
محمود بهبودي، بهرام رنگي پور
استاد مشاور :
محمدرضا ودادي
استاد داور :
حسين خبازيان، عاطفه قرباني
