TY  - BOOK
AU  - Buium,Alexandru
ED  - SpringerLink (Online service)
TI  - Differential Algebraic Groups of Finite Dimension
T2  - Lecture Notes in Mathematics,
SN  - 9783540467649
AV  - QA564-609 
U1  - 516.35 23
PY  - 1992///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Mathematics
KW  - Geometry, algebraic
KW  - Group theory
KW  - Algebraic Geometry
KW  - Group Theory and Generalizations
N1  - Terminology and conventions -- First properties -- Affine D-group schemes -- Commutative algebraic D-groups -- General algebraic D-groups -- Applications to differential algebraic groups
N2  - Differential algebraic groups were introduced by P. Cassidy and E. Kolchin and are, roughly speaking, groups defined by algebraic differential equations in the same way as algebraic groups are groups defined by algebraic equations. The aim of the book is two-fold: 1) the provide an algebraic geometer's introduction to differential algebraic groups and 2) to provide a structure and classification theory for the finite dimensional ones. The main idea of the approach is to relate this topic to the study of: a) deformations of (not necessarily linear) algebraic groups and b) deformations of their automorphisms. The reader is assumed to possesssome standard knowledge of algebraic geometry but no familiarity with Kolchin's work is necessary. The book is both a research monograph and an introduction to a new topic and thus will be of interest to a wide audience ranging from researchers to graduate students
UR  - http://dx.doi.org/10.1007/BFb0087235
ER  -