By Alfonso Di Bartolo,Giovanni Falcone,Peter Plaumann,Karl Strambach
Algebraic teams are taken care of during this quantity from a gaggle theoretical viewpoint and the received effects are in comparison with the analogous concerns within the idea of Lie teams. the most physique of the textual content is dedicated to a class of algebraic teams and Lie teams having in simple terms few subgroups or few issue teams of alternative style. specifically, the range of the character of algebraic teams over fields of optimistic attribute and over fields of attribute 0 is emphasised. this can be printed via the plethora of third-dimensional unipotent algebraic teams over an ideal box of optimistic attribute, in addition to, through many concrete examples which disguise a space systematically. within the ultimate part, algebraic teams and Lie teams having many closed basic subgroups are determined.
Read or Download Algebraic Groups and Lie Groups with Few Factors (Lecture Notes in Mathematics) PDF
Best group theory books
This article bargains a rigorous creation into the idea and strategies of convergence areas and offers concrete purposes to the issues of useful research. whereas there are a couple of books facing convergence areas and a very good many on useful research, there are none with this actual concentration.
It turned increasingly more traditional, from, say, the Nineteen Seventies, for every ebook on Module concept, to show and turn out a few (but in not more than 15 to twenty pages) generalizations to (mostly modular) lattices. This used to be justified by way of the these days greatly accredited notion that the constitution of a module over a hoop is better understood by way of the lattice struc ture of its submodule lattice.
Deligne-Lusztig idea goals to check representations of finite reductive teams via geometric tools, and especially l-adic cohomology. many fantastic texts current, with diverse pursuits and views, this idea within the normal atmosphere. This publication specializes in the smallest non-trivial instance, particularly the crowd SL2(Fq), which not just offers the simplicity required for an entire description of the idea, but additionally the richness wanted for illustrating the main smooth points.
Supplying an almost entire number of up to date equipment and effects on block invariants with recognize to their disorder teams, this e-book covers the classical conception pioneered by way of Brauer, the trendy idea of fusion platforms brought via Puig, the geometry of numbers built via Minkowski, the type of finite basic teams, and diverse machine assisted equipment.
Extra resources for Algebraic Groups and Lie Groups with Few Factors (Lecture Notes in Mathematics)
Algebraic Groups and Lie Groups with Few Factors (Lecture Notes in Mathematics) by Alfonso Di Bartolo,Giovanni Falcone,Peter Plaumann,Karl Strambach