query: Algebraic complex groups and reductive algebraic groups
positive_passages.docid: 21057
positive_passages.text: Complex algebraic group is reductive $\iff$ it is the complexification of a compact Lie group?
negative_passages.docid: 148310
negative_passages.text: Showing rational numbers are algebraic
negative_passages.docid: 148203
negative_passages.text: The genus of an algebraic curve is invariant under isomorphisms
negative_passages.docid: 126094
negative_passages.text: Hartshorne Algebraic Geometry Exercise II.2.16.
negative_passages.docid: 84869
negative_passages.text: Are the groups $\mathbb{C}$ and $\mathbb{R}$ isomorphic?
negative_passages.docid: 57283
negative_passages.text: Extending Homomorphism into Algebraically Closed Field
negative_passages.docid: 28079
negative_passages.text: Do these definitions of irreducibility of algebraic sets coincide?
negative_passages.docid: 5599
negative_passages.text: Proving an inclusion for the derived group
negative_passages.docid: 153250
negative_passages.text: Finding the derived group
negative_passages.docid: 79679
negative_passages.text: Let $\alpha, \beta \in \mathbb{C}$, such that $\alpha + \beta$, and $\alpha\beta$ are algebraic. Show that $\alpha$ and $\beta$ are algebraic.
negative_passages.docid: 38571
negative_passages.text: Localization of a total quotient ring of a reduced ring
negative_passages.docid: 63605
negative_passages.text: Irreducible polynomials and affine variety
negative_passages.docid: 68717
negative_passages.text: Complete reducibility of a representation of a lie algebra
negative_passages.docid: 33455
negative_passages.text: Question on group homomorphisms involving the standard Z-basis
negative_passages.docid: 30236
negative_passages.text: isomorphic groups related in direct product.
negative_passages.docid: 4000
negative_passages.text: If every polynomial of degree 2 is reducible then $K$ is algebraically closed?
negative_passages.docid: 146028
negative_passages.text: $GL(n, \mathbb{C})$ is isomorphic to a subgroup of $GL(2n, \mathbb{R})$