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National Repository of Grey Literature 2 records found  Search took 0.00 seconds. 
Inverse limits in module categories
 Menčík, Matouš ; Trlifaj, Jan (advisor) ; Šaroch, Jan (referee)
For a class of modules C, we study the class lim ←− C of modules that can be obtained as inverse limits of modules from C. In particular, we investigate how additional properties of the class C are reflected by properties of the class lim ←− C. We also address the question of whether for a given module M, every inverse limit of products of M is an inverse limit of finite products of M. We provide examples of modules for which the answer is positive, negative, and for which there is a reason to believe that it depends on additional set-theoretic assumptions. 1
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The classical McKay correspondence
 Menčík, Matouš ; Šťovíček, Jan (advisor) ; Shaul, Liran (referee)
The McKay correspondence is an interesting connection between many different areas of mathematics. The connecting element of the McKay correspondence is a special family of graphs called the Dynkin diagrams. In this thesis, we will study the classical McKay correspondence, which is an interesting connection between finite subgroups of SL(2,C) and Dynkin diagrams without oriented edges. Moreover, there are two ways how to get the Dynkin diagrams from the groups. In the first chapter of the thesis, we will provide a classification for both the finite subgroups and Dynkin diagrams. The second chapter uses the tools of the representation theory to construct the corresponding graph from the irreducible representations of the group. In the third part, we let the group act on the two-dimensional complex vector space. We then factor out this action to construct an algebraic variety with one singular point and find the Dynkin diagram in this singularity. 1
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See also: similar author names
1 Menčík, Michal
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