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Twistor operator in symplectic spin geometry
Dostálová, Marie ; Krýsl, Svatopluk (advisor) ; Doubek, Martin (referee)
The topic of the diploma thesis is symplectic spinor geometry. Its re- search was started by D. Shale, B. Kostant and K. Habermann. We focus our attention to one of the so called symplectic twistor operators introduced by S. Kr'ysl. We investigate the action of this operator on real even dimensio- nal vector spaces considered as symplectic manifold, its invariance properties and regularity. We describe a part of the kernel of the symplectic twistor operator when acting on symplectic spinors on R2. The kernel forms a repre- sentation of the so called metaplectic group (double cover of the symplectic group). 1
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Tilting theory of commutative rings
Hrbek, Michal ; Trlifaj, Jan (advisor) ; Herbera Espinal, Dolors (referee) ; Šaroch, Jan (referee)
The thesis compiles my contributions to the tilting theory, mainly in the set- ting of a module category over a commutative ring. We give a classification of tilting classes over an arbitrary commutative ring in terms of data of geometrical flavor - certain filtrations of the Zariski spectrum. This extends and connects the results known previously for the noetherian case, and for Prüfer domains. Also, we show how the classes can be expressed using the local and Čech homology the- ory. For 1-tilting classes, we explicitly construct the associated tilting modules, generalizing constructions of Fuchs and Salce. Furthermore, over any commuta- tive ring we classify the silting classes and modules. Amongst other results, we exhibit new examples of cotilting classes, which are not dual to any tilting classes - a phenomenon specific to non-noetherian rings. 1
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Tilting theory of commutative rings
Hrbek, Michal ; Trlifaj, Jan (advisor) ; Herbera Espinal, Dolors (referee) ; Šaroch, Jan (referee)
The thesis compiles my contributions to the tilting theory, mainly in the set- ting of a module category over a commutative ring. We give a classification of tilting classes over an arbitrary commutative ring in terms of data of geometrical flavor - certain filtrations of the Zariski spectrum. This extends and connects the results known previously for the noetherian case, and for Prüfer domains. Also, we show how the classes can be expressed using the local and Čech homology the- ory. For 1-tilting classes, we explicitly construct the associated tilting modules, generalizing constructions of Fuchs and Salce. Furthermore, over any commuta- tive ring we classify the silting classes and modules. Amongst other results, we exhibit new examples of cotilting classes, which are not dual to any tilting classes - a phenomenon specific to non-noetherian rings. 1
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Algorithms in Representation Theory
Trunkát, Marek ; Šťovíček, Jan (advisor) ; Růžička, Pavel (referee)
This thesis deals with an implementation of algorithm for computation of generator of almost split sequences ending at an indecomposable nonprojective module of path algebra over finite quiver. Algorithm is implemented in algebra system GAP (Groups, Algorithms, Programming) with additional package QPA (Quivers and Path Algebras). Powered by TCPDF (www.tcpdf.org)
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Twistor operator in symplectic spin geometry
Dostálová, Marie ; Krýsl, Svatopluk (advisor) ; Doubek, Martin (referee)
The topic of the diploma thesis is symplectic spinor geometry. Its re- search was started by D. Shale, B. Kostant and K. Habermann. We focus our attention to one of the so called symplectic twistor operators introduced by S. Kr'ysl. We investigate the action of this operator on real even dimensio- nal vector spaces considered as symplectic manifold, its invariance properties and regularity. We describe a part of the kernel of the symplectic twistor operator when acting on symplectic spinors on R2. The kernel forms a repre- sentation of the so called metaplectic group (double cover of the symplectic group). 1
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