Radical of an Algebraic Group

Herausgegeben:Surhone, Lambert M.; Tennoe, Mariam T.; Henssonow, Susan F.

• Broschiertes Buch

Produktbeschreibung

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, an algebraic group G contains a unique maximal normal solvable subgroup; and this subgroup is closed. Its identity component is called the radical of G. In algebraic geometry, an algebraic group (or group variety) is a group that is an algebraic variety, such that the multiplication and inverse are given by regular functions on the variety. In category theoretic terms, an algebraic group is a group object in the category of algebraic varieties. Two important classes of algebraic groups arise, that for the most part are studied separately: abelian varieties (the ''projective'' theory) and linear algebraic groups (the ''affine'' theory). There are certainly examples that are neither one nor the other these occur for example in the modern theory of integrals of the second and third kinds such as the Weierstrass zeta function, or the theory of generalized Jacobians. But according to a basic theorem any algebraic group is an extension of an abelian variety by a linear algebraic group.

Produktdetails

• Verlag: Betascript Publishing
• Seitenzahl: 72
• Englisch
• Abmessung: 220mm
• ISBN-13: 9786131244629
• ISBN-10: 6131244626
• Artikelnr.: 30041248