Picard group of a connected affine algebraic group
Copyright policy )Picard group of a connected affine algebraic group
We prove that the Picard group of a connected affine algebraic group $G$ is isomorphic to the fundamental group of the derived subgroup of the reductive algebraic group $G/{\mathscr R}_u(G)$, where ${\mathscr R}_u(G)$ is the unipotent radical of $G$.
Revised version emphasizing the canonical nature of the construction. 4 pages
- National Research University Higher School of Economics Russian Federation
Affine algebraic groups, hyperalgebra constructions, connected affine algebraic groups, Mathematics - Algebraic Geometry, group varieties, unipotent radical, Picard groups, FOS: Mathematics, reductive algebraic groups, Algebraic Geometry (math.AG)
Affine algebraic groups, hyperalgebra constructions, connected affine algebraic groups, Mathematics - Algebraic Geometry, group varieties, unipotent radical, Picard groups, FOS: Mathematics, reductive algebraic groups, Algebraic Geometry (math.AG)
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