On central extensions of simple differential algebraic groups

2014/01/02 by Minchenko, Andrei
#Commutative Algebra (math.AC) #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1401.0522

Abstract

We consider central extensions Z\hookrightarrow E\twoheadrightarrow G in the category of linear differential algebraic groups. We show that if G is simple non-commutative and Z is unipotent with the differential type smaller than that of G, then such an extension splits. We also give a construction of central extensions illustrating that the condition on differential types is important for splitting. Our results imply that non-commutative almost simple linear differential algebraic groups, introduced by Cassidy and Singer, are simple.

Related

• Differential Central Simple Algebras
• A Jordan-Hoelder Theorem for Differential Algebraic Groups
• Differential Galois Groups of Differential Central Simple Algebras and their Projective Representations
• The automorphisms of differential extensions of characteristic p
• Galois Groups of Linear Difference-Differential Equations