A Novel Categorical Approach to the Classification of Semi Simple Algebraic Groups
Keywords:
Semi-simple algebraic groups Tannakian categories Gerbes Coho- mological invariants Lie algebras Group schemesAbstract
We present a novel categorical framework for the classification of semi-simple algebraic groups over algebraically closed fields of characteristic zero. By inte- grating Tannakian duality with modern cohomological methods, we provide new insights into the connections between semi-simple algebraic groups, their repre- sentation categories, and associated geometric structures. Our approach empha- sizes the role of fiber functors, gerbes, and cohomological invariants in capturing the essential features of these groups, leading to a more unified and conceptual understanding of their classification.
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